**Course: **MATH 2110

**Title: **Introductory Geometry for Middle School Teachers

**Section: **100 (Class Number 7969)

**Campus: **Ohio University, Athens Campus

**Department: **Mathematics

**Academic Year: **2019 - 2020

**Term: **Fall Semester

**Instructor: **Mark Barsamian

**Contact Information: **My contact information is posted on my web page.

**Office Hours for 2019 - 2020 Fall Semester: **8:45am - 9:30am Mon - Fri in Morton 538

**Course Description: **Intended for Middle Childhood Education majors. Core concepts and principles of Euclidean geometry in two- and three-dimensions. Informal and formal proof. Measurement. Properties and relations of geometric shapes and structures. Symmetry. Transformational geometry. Tessellations. Congruence and similarity. Coordinate geometry. Constructions. Historical development of Euclidean and non-Euclidean geometries including contributions from diverse cultures. Dynamic Geometry Software to build and manipulate representations of two- and three- dimensional objects.

**Prerequisites: **(MATH 1300 or 1322 or Math placement level 3) and education major

**Special Needs: **If you have physical, psychiatric, or learning disabilities that require accommodations, please let me know as soon as possible so that your needs may be appropriately met.

**Class meetings: **Mon, Wed, Fri 9:40am - 10:35am in Morton Hall Room 223

**Final Exam Date: **Friday, December 13, 2018, 8:00am - 10:00am in Morton 223

**Syllabus: **For Section 100 (Class Number 7969), taught by Mark Barsamian, this web page replaces the usual paper syllabus. If you need a paper syllabus (now or in the future), unhide the next four portions of hidden content (Textbook, Calendar, Grading, Course Structure) and then print this web page.

**Textbook Information: **

**Title: ***College Geometry, 2 ^{nd} Edition*

**Authors: **Musser, Trimpe, Maurer

**Publisher: **Pearson, 2008

**ISBN Numbers: **

**Hardcover ISBN-10:**0131879693**Hardcover ISBN-13:**978-0131879690**Loose Leaf ISBN-10:**0321656776**Loose Leaf ISBN-13:**978-0321656773

**Calendar: **

**Day #1:**1.1 Problem-Solving Strategies**Topic:**1.1 Problem-Solving Strategies**Book Section:**1.1 Problem-Solving Strategies**Exercises:**Section 1.1 # 3, 5, 7, 11, 17, 19, 23, 25, 33, 39

**Day #2:**1.2 More Problem-Solving Strategies**Topic:**1.2 More Problem-Solving Strategies**Book Section:**1.2 More Problem-Solving Strategies**Class Presentations (CP1): (Have your presentation written large and clear on paper, ready to project on a document camera.)**- Class Presentation: Present 1.2 # 4 (observing simple patterns)
- Class Presentation: Present 1.2 # 6 (observing simple patterns)
- Class Presentation: (Present 1.2 # 26 (observing simple patterns)
- Class Presentation: Present 1.2 # 18 (make a table)
- Class Presentation: Present 1.2 # 19 (make a table)

**Exercises:**Section 1.2 # 5, 7, 9, 15, 19, 21, 23, 25, 27, 29, 33, 35, 37, 39, 41

**Day #3:**2.1 Undefined Terms, Definitions, Postulates, Segments, Angles**(Quiz 1)****Topic:**2.1 Undefined Terms, Definitions, Postulates, Segments, Angles**Book Section:**2.1 Undefined Terms, Definitions, Postulates, Segments, Angles**Class Presentations (CP1): (Have your presentation written large and clear on paper, ready to project on a document camera.)**- Class Presentation: Present solution to 2.1 # 17 (solving 2 equations in 2 unknowns involving angles)
- Class Presentation: Present solution to 2.1 # 18 (solving 2 equations in 2 unknowns involving angles)
- Class Presentation: Present solution to 2.1 # 19 (solving 2 equations in 2 unknowns involving angles)
- Class Presentation: Present solution to 2.1 # 21 regions created by n lines
- Class Presentation: Present solution to 2.1 # 22 greatest number of lines through n points

**Exercises:**Section 2.1 # 7, 11, 15, 17, 19, 21, 22, 39, 42**Quiz 1**

**Day #4:**2.2 Polygons and Circles**Topic:**2.2 Polygons and Circles**Book Section:**2.2 Polygons and Circles**Class Presentations (CP1): (Have your presentation written large and clear on paper, ready to project on a document camera.)**- Class Presentation: 2.2 #4 draw shapes of specified types
- Class Presentation: 2.2 # 6 involving constructing triangles with 11 toothpicks
- Class Presentation: 2.2 # 20 drawing rectangles on a lattice
- Class Presentation: 2.2 # 22 drawing shapes with vertices at given points on a circle
- Class Presentation: 2.2 #28 involving symmetry

**Exercises:**Section 2.2 # 3, 5, 7, 11, 15, 19, 21, 27, 29, 31, 33, 35

**Day #5:**2.3 Angle Measure in Polygons and Tessalations**Topic:**2.3 Angle Measure in Polygons and Tessalations**Book Section:**2.3 Angle Measure in Polygons and Tessalations**Class Presentations: (Have your presentation written large and clear on paper, ready to project on a document camera.)**- Class Presentation:: 2.3#2 make copies of a triangle to form a tesselation
- Class Presentation:: 2.3#4c about tesselation
- Class Presentation:: 2.3#6b involving angle sum
- Class Presentation:: 2.3#12d involving angle sum and variable
- Class Presentation: 2.3#20 given vertex angle of regular n-gon, find n

**Exercises:**Section 2.3 # 1, 3, 9, 11d,13, 15, 19, 21, 23, 25, 33

**Day #6:**2.4 Three-Dimensional Shapes**(Quiz 2)****Topic:**2.4 Three-Dimensional Shapes**Book Section:**2.4 Three-Dimensional Shapes**Class Presentations: (Have your presentation written large and clear on paper, ready to project on a document camera.)**- Class Presentation: 2.4 # 6 Present a solution to book exercise 2.4 # 6. Figure out which hexominoes can be folded up to form a cube. Present a drawing of all those hexominoes (all on one page). Chose one of those hexominoes and make a big drawing of your that one hexomino, and have it pre-cut and show in class how it can be folded up into a cube.
- Class Presentation: Two parts:
- Present a solution to book exercise 2.4 # 16abc Which of the drawings in a,b,c is a net for a square pyramid? For the drawings that are, make a big drawing of the net. Have your nets pre-cut and show how they can be folded up into a pyramid.
- Draw a net for a square pyramid that is
*not*one of the drawings in 2.4 # 16abc. Have your net pre-cut and show how it can be folded up into a pyramid.

- Class Presentation: 2.4 # 24 Euler Formula for pyramids
- Class Presentation: 2.4 # 28 Polyhedron has 10 edges and 6 vertices. How many faces does it have? Sketch a polyhedron that satisfies these conditions and name it.

**Exercises:**Section 2.4 # 1, 3, 5, 9, 11, 15, 17, 19, 21, 23, 25, 27, 29, 33, 35, 37**Quiz 2**

**Day #7:**2.5 Dimensional Analysis**Topic:**2.5 Dimensional Analysis**Book Section:**2.5 Dimensional Analysis**Class Presentations: (You will use the***chalkboard*for this one,*not*the*document camera*.)**Simple Conversions involving Converting Only One Unit:**- Class Presentation: 2.5 Review #2 (p.99) converting gallons to tablespoons

**More Sophisticated Conversions Involving Converting Ratios of Units:**- Class Presentation: 2.5 # 18 converting 90 cm/day to ft/hour
- Class Presentation: 2.5 # 23 converting ½ inch per 4 weeks to mph
- Class Presentation: 2.5 Review #4 (p.99) convert 8 eight-oz glass/day to liters per year
- Class Presentation: 2.5 Review #5 (p.99) convert 100 km/hour to m/sec
- Class Presentation: Ch 2 Test #21 (p.100) convert 6 oz/ft^3 to grams/liter

**More Complicated Problems:**- Class Presentation: 2.5 #22. Given gas price ($/gal) & tank (liters) how much to fill tank?
- Class Presentation: Ch 2 Test #23 (p. 101) audio CD revolutions

**Exercises:**Section 2.5 # 5, 7, 9, 11, 13, 17, 19, 23, 25, 27

**Day #8:****In-Class Exam 1 on Chapters 1 - 2****Take Home Problem:**Make a Venn Diagram showing relationship between the following 14 classes of three-dimensional shapes. (These classes are introduced in Section 2.4 of the textbook.) Include one drawing of a sample shape in each region of the diagram.- Polyhedra
- Regular Polyhedra
- Prisms
- Right Prisms
- Oblique Prisms
- Pyramids
- Right Regular Pyramid
- Oblique Regular Pyramid
- Circular Cylinder
- Right Circular Cylinder
- Oblique Circular Cylinder
- Circular Cone
- Right Circular Cone
- Oblique Circular Cone.

**Day #9:**3.1 Perimeter, Circumference, Area of Rectangles & Triangles**Topic:**3.1 Perimeter, Circumference, Area of Rectangles & Triangles**Book Section:**3.1 Perimeter, Circumference, Area of Rectangles & Triangles**Class Presentations:****Class Presentations:**- Class Presentation: (Generalization of 3.1#11 about area, perimeter, circumference, radius of square, circle) (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown area
*A*. - Then substitute the particular value
*A*= 25*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
- Class Presentation: (Generalization of 3.1#11 about area, perimeter, circumference, radius of square, circle) (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown area
*A*. - Then substitute the particular value
*A*= 18.45*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
- Class Presentation: (Generalization of 3.1#17 about perimeter of rectangle, need to introduce variable) (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown perimeter
*P* - Then substitute the particular value
*P*= 72*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown perimeter
- Class Presentation: (Generalization of 3.1#18 about area of rectangle, need to introduce variable) (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown area
*A* - Then substitute the particular value
*A*= 1440*cm*^{2}into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown area
- Class Presentation: (Generalization of 3.1#13b)
Make a large copy of the figure in exercise 3.1#13(b) that you can project using the document camera.
- Find the area by using the area of smaller shapes. Explain how you get your answer.
- Find the area again, but this time use
*Pick's Theorem*(See Exercise 3.1#38). Present your calculation.

- Class Presentation: (Generalization of 3.1#11 about area, perimeter, circumference, radius of square, circle) (Present your work on the chalkboard.)

**Exercises:**Section 3.1 # 5, 7, 11, 13, 17, 19, 20, 27, 28, 31, 33, 35, 37, 38, 51

**Day #10:**3.2 More Area Formulas**Topic:**3.2 More Area Formulas**Book Section:**3.2 More Area Formulas**Class Presentations:**- Class Presentation about area of region between concentric regular hexagons. Present a solution to a general version of 3.2#14 (on the chalkboard.)
- First, present an analytical solution, using an unknown length
*OP*and known length*PQ*= 1 - Then substitute the particular value
*OP*= 5.3*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown length
- Class Presentation about area of region created by overlapping circles: Present a solution to a general version of 3.2#16 (on the chalkboard.)
- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 10.5*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
- Class Presentation about area of region created by overlapping circle and square: Present a solution to a general version of 3.2#18a (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 5*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
- Class Presentation about area of region between butting circles: Present a solution to a general version of 3.2#18b (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown radius
*R*. - Then substitute the particular value
*R*= 1*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown radius
- Class Presentation about area of region created by overlapping circles: Present a solution to a general version of 3.2#19 (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown side length
*x*. - Then substitute the particular value
*x*= 8*cm*into your general analytical solution to answer the book question.

- First, present an analytical solution, using an unknown side length

- Class Presentation about area of region between concentric regular hexagons. Present a solution to a general version of 3.2#14 (on the chalkboard.)
**Exercises:**Section 3.2 # 1, 9, 13, 14, 16, 17, 18, 19, 21, 22, 23, 36, 39, 43

**Day #11:**3.3 The Pythagorean Theorem and Right Triangles**Topic:**3.3 The Pythagorean Theorem and Right Triangles**Book Section:**3.3 The Pythagorean Theorem and Right Triangles**Class Presentations:**#### Problems about Equilateral Triangles

(Present your work on the chalkboard.)- Class Presentation: (Given side length of equilateral triangle, find its area) Present a solution to 3.3#24 (Make a diagram and show the steps clearly.)
- Class Presentation: (Given altitude of equilateral triangle, find its area) Present a solution to 3.3#23 (Make a diagram and show the steps clearly.)

#### Problems about Regular Hexagons

(Present your work on the chalkboard.)- Class Presentation: (Given side length for regular hexagon, what is its area?) A regular hexagon has sides of length x. What is the area A of the hexagon? (Make a diagram and show the steps clearly.)
- Class Presentation: (Given area for regular hexagon, what is its side length?) A regular hexagon has area A. What is the length x of the sides of the hexagon? (Make a diagram and show the steps clearly.)
- Class Presentation: (Given altitude of regular hexagon, find its area) Present a solution to a general version of 3.3#21 (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown distance h. (Make a diagram and show the steps clearly.)
- Then substitute particular value \( h = 10\sqrt{3} \) into your general solution to answer book question.

- Class Presentation: (Given radius of regular hexagon, find its area) Present a solution to a general version of 3.3#22 (Present your work on the chalkboard.)
- First, present an analytical solution, using an unknown radius R (Make a diagram and show the steps clearly.)
- Then substitute particular value R=15 into your general solution to answer book question.

**Exercises:**Section 3.3 # 2, 4, 9, 12, 13, 14, 22, 23, 24, 25, 30, 35, 48, 49

**Day #12:**3.4 Surface Area**(Quiz 3)****Topic:**3.4 Surface Area**Book Section:**3.4 Surface Area**Class Presentations:****Surface area of prism and pyramid with same base.****Jenna Baratie:**(Similar to 3.4#3a)- A right prism has height
*h*and has a base that is an equilateral triangle with sides of length*x*. Draw the prism and find its surface area. - Now suppose that the height is 7 and the base has side length 5. Find the surface area.

- A right prism has height
**Ashley Benedict:**(Related to 3.4#3a)- A right pyramid has sides with slant height
*L*and has a base that is an equilateral triangle with sides of length*x*. Draw the pyramid and find its surface area. - Now suppose that the slant height is 7 and the base has side length 5. Find the surface area.

- A right pyramid has sides with slant height

**Surface area of right pyramids, one with given slant height and one with given height.****Sam Bernstein:**(Similar to 3.4#8a)- A right pyramid has a base that is a square with sides of length
*x*and has slant height*L*. Draw the pyramid and find its surface area. - Now suppose that the base has side length 5 and the slant height is 7. Find the surface area.

- A right pyramid has a base that is a square with sides of length
**Audrey Brown:**(Similar to 3.4#12)- A right pyramid has a base that is a rectangle that has sides of length 2
*a*and 2*b*and has height*h*. Draw the pyramid and find its surface area. - Now suppose that the base has sides of length length 10 and 18 and the height is 12. Find the surface area. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)

- A right pyramid has a base that is a rectangle that has sides of length 2

**Surface area of right circular cones, one with given slant height and one with given height.****Dominic Buttari:**(Similar to 3.4#17a)- A right circular cone has base radius
*4*and has slant height*L*. Draw the cone and find its surface area. - Now suppose that the base has radius 5 and the slant height is 13. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.

- A right circular cone has base radius
**Kaitlin Cozad:**(Similar to 3.4#12)- A right circular cone has base radius
*r*and has height*h*. Draw the cone and find its surface area. - Now suppose that the base has radius 9 and the height is 12. Find the surface area. Give an exact answer in symbols, and then a decimal approximation.

- A right circular cone has base radius

**Surface area of sphere****Annie Dill:**Present a solution to to 3.4 # 29, but instead of dimensions 1.25 and 1.86 shown in the picture, use numbers 4 and 7. Give an exact answer in symbols. Then give a decimal approximation

**Exercises:**Section 3.4 # 3, 8, 12, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29 (*EAFTDA*)**Quiz 3**

**Day #13:**3.5 Volume**Topic:**3.5 Volume**Book Section:**3.5 Volume**Class Presentations:****Problems involving volumes of cones and pyramids****Jessie Feilen:**(Similar to 3.5#10) A right pyramid has a base that is a regular pentagon that has the following attributes:- The sides of the base have length
*L*= 2*a* - The perpendicular distance from the center of the base to one of its sides is
*b*. - The height is
*h*.

- Draw the pyramid and find its volume.
- Now suppose that
*a*= 5 and*b*= 18 and*h*= 12. Find the volume. Give an exact, simplified answer, not a decimal approximation. (Hint: There are some famous triangles involved, whose sides can be determined without a calculator!)

- The sides of the base have length
**Hanna Gerrard:**Present a solution to 3.5 #13 about the volume of right circular cones. For both (a) and (b) of the problem, do the following:- Present an answer in exact, simplified form without using a calculator
- Then type your exact answer into a calculator to get a decimal approximation, rounded to two decimal places.

**Problems about involving the volume of a hollow shape.****Zack Graham:**(based on 3.5 # 41 about volume of rubber in a tennis ball)- Use circumference
*C*cm and thickness*T*cm. - Use circumference
*C*= 22 cm and thickness*T*= 0.6 cm. Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.) Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.

- Use circumference
**Katie Henry:**Present a solution to 3.5#44 about a steel pipe. Give exact answers in symbols, ready to type into a calculator. Then use a calculator to get decimal approximations rounded to two decimal places

**Problems involving Unit Conversions.****Gwen Hoshor:**(similar to 3.5#17c) Convert 0.47 ft^{3}to cm^{3}- Present the answer as an exact expression that is ready to type into a calculator. (Exact! Not a decimal approximation.)
- Then type the expression into a calculator to get a decimal approximation rounded to two decimal places.
- Present the conversion as a single line equation (like we did in class).

**Amira Hunter:**(Related to 3.5#43 about pumping liquid out of a spherical tank)- The book's presentation of the problem says to
*recall that 1 ft*. What is the exact conversion? (Show how it is obtained.) (Use the fact that the US gallon is legally defined as 231 cubic inches.)^{3}≈ 7.48 gal - Present a solution 3.5 # 43 but use diameter
*D*ft and liquid volume*G*gallons, and use the exact conversion of ft^{3}to gallons that you found in part (a). - Now find the answer when
*D*= 6 ft liquid volume*G*= 200 gallons. Give an exact answer in symbols, ready to type into a calculator. Then use a calculator to get a decimal approximation rounded to two decimal places

- The book's presentation of the problem says to

**Problems involving Scaling.****Matthew McFarland:**(similar to 3.5#22) How much do the surface area and volume of a sphere change if its radius is doubled? If its radius is multiplied by some constant*k*? Explain.**Brianna McFee:**(similar to 3.5#23) How do the surface area and volume of a rectangular box change if its*length*,*width*, and*height*are all doubled? If they are multiplied by some constant*k*? Explain.

**Exercises:**Section 3.5 Volume # 3, 7, 13, 17, 22, 23, 28, 41, 43, 44, 45, 46 (*EAFTDA*)

**Day #14:**4.1 Reasoning and Proof in Geometry**Topic:**4.1 Reasoning and Proof in Geometry**Book Section:**4.1 Reasoning and Proof in Geometry**Reference:**List of Postulates and Theorems**Class Presentations:****For Lilly Michigan, Mitchell Myers, Trystan Peyton, Laura Rodgers:**Consider the following list of statements that are all named*S*:- Statement
*S*: If two angles share a common vertex, then they are adjacent - Statement
*S*: If a polygon is regular, the the polygon has all angles congruent - Statement
*S*: If a polygon has a vertex angle of measure 60, then the polygon is a triangle - Statement
*S*: If a triangle has two angles that are complementary, then the triangle is a right triangle

Answer the following questions

**Lilly:**Which conditional Statement*S*has the property that*S*is true and the converse of*S*is also true? Explain.**Mitchell:**Which conditional Statement*S*has the property that*S*is true but the converse of*S*is false? Explain.**Trystan:**Which conditional Statement*S*has the property that*S*is false but the converse of*S*is true? Explain.**Laura:**Which conditional Statement*S*has the property that*S*is false and the converse of*S*is also false? Explain.

**For Conner Singleton, Hannah Six, Lindsay Stanton, Sydney Waugh:**Consider the following new list of statements that are also all named*S*:- Statement
*S*: If a triangle has reflection symmetry, then the triangle is isosceles - Statement
*S*: Given a triangle with sides of length 2 and 5, If the third side has length 5, then the triangle is isosceles - Statement
*S*: If a triangle has sides 8,13,15, then the triangle is a right triangle - Statement
*S*: If two angles share a common vertex and a common side, then they are adjacent.

Answer the following questions

**Conner:**Which conditional Statement*S*has the property that*S*is true and the converse of*S*is also true? Explain.**Hannah:**Which conditional Statement*S*has the property that*S*is true but the converse of*S*is false? Explain.**Lindsay:**Which conditional Statement*S*has the property that*S*is false but the converse of*S*is true? Explain.**Sydney:**Which conditional Statement*S*has the property that*S*is false and the converse of*S*is also false? Explain.

**Tyler Wulf:**(The sophisticated problem for today. Sorry.) We have discussed in class the idea the for a conditional statement*S*of the form*If P then Q*, there are three associated conditional statements:*The contrapositive of S*is the statement*If not Q then not P*.*The converse of S*is the statement*If Q then P*.*The inverse of S*is the statement*If not P then not Q*.

We have discussed in class that the

*contrapositive of S*is logically equivalent to*S*. That is, either they are both true, or they are both false.And we have discussed in class that

*converse of S*is not logically equivalent to*S*. The truth (or untruth) of one of them tells us nothing about the truth (or untruth) of the other.But what about the

*inverse of S*? How is the truth of*The inverse of S*related to the truth of*S*and the truth of the*contrapositive of S*and the truth of the*converse of S*? Explain.- Statement
**Exercises:**Section 4.1 Reasoning and Proof in Geometry # 17, 18, 19, 20, 22, 25, 26, 27, 8, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 45

**Day #15:**4.2 Triangle Congruence Relations**(Quiz 4)****Topic:**4.2 Triangle Congruence Relations**Book Section:**4.2 Triangle Congruence Relations**Reference:**List of Postulates and Theorems**Class Presentations:****Jenna Baratie:**Solve 4.2 # 19 about proving two triangles are congruent.**Ashley Benedict:**Solve 4.2 # 33 about proving that two angles are congruent.**Sam Bernstein:**Solve 4.2 # 35 which asks you to prove that in a rhombus, the diagonal divides the rhombus into two congruent triangles.**Audrey Brown:**Solve 4.2 # 41 about proving that two angles are congruent.

**Exercises:**Section 4.2 # 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 35, 37, 40, 42**Quiz 4**

**Day #16:**4.3 Problem Solving Using Triangle Congruence**Topic:**4.3 Problem Solving Using Triangle Congruence**Book Section:**4.3 Problem Solving Using Triangle Congruence**Reference:**List of Postulates and Theorems**Class Presentations:****Dominic Buttari:**Solve 4.3 # 4 about finding the measure of two angles, but use ∠*ADE*=*x*and ∠*BAC*=*y***Kaitlin Cozad:**Solve 4.3 # 9 about proving that two segments are congruent.**Annie Dill:**Solve 4.3 # 11 about proving two triangles are congruent.

**Exercises:**Section 4.3 # 3, 5, 7, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20

**Friday is Fall Break: No Class**

**Day #17:**4.3 Problem Solving Using Triangle Congruence, continued**Topic:**4.3 Problem Solving Using Triangle Congruence**Book Section:**4.3 Problem Solving Using Triangle Congruence**Reference:**List of Postulates and Theorems**Class Presentations:****Jessie Feilen:**Book Problem 4.3#13 is worded as follows:- In triangle \( \Delta ABC \), \( \overline{BD} \) is an altitude of \( \Delta ABC \) and also the bisector of angle \( \angle B \). Prove that \( \overline{BD} \) is the perpendicular bisector of side \( \overline{AC} \).

- Prove that given any triangle \( \Delta ABC \) with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects angle \( \angle ABC \) and \( \overline{BD} \) is perpendicular to side \( \overline{AC} \), then \( \overline{BD} \) bisects side \( \overline{AC} \).

**Hanna Gerrard:**Book Problem 4.3#15 is worded as follows:- Prove that in any isosceles triangle, the median drawn from the vertex angle is the perpendicular bisector of the opposite side.

- Prove that given any triangle \( \Delta ABC \) with \( \overline{BA} \cong \overline{BC} \) and with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects side \( \overline{AC} \), then \( \overline{BD} \) is perpendicular to side \( \overline{AC} \).

**Zack Graham:**Book Problem 4.3#16 is worded as follows:- Prove that in any isosceles triangle, the median drawn from the vertex angle is the bisector of that angle.

- Prove that given any triangle \( \Delta ABC \) with \( \overline{BA} \cong \overline{BC} \) and with a point \( D \) on side \( \overline{AC} \), if \( \overline{BD} \) bisects side \( \overline{AC} \), then \( \overline{BD} \) bisects angle \( \angle ABC \).

**Exercises:**Section 4.3 # 3, 5, 7, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20

**Day #18:****In-Class Exam 2 Covering Chapters 3 - 4****Day #19:**5.1 Indirect Reasoning and the Parallel Postulate**Topic:**5.1 Indirect Reasoning and the Parallel Postulate**Book Section:**5.1 Indirect Reasoning and the Parallel Postulate**Reference:**List of Postulates and Theorems**Class Presentations Assignments Postponed to Monday****Exercises:**Section 5.1 # 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 29, 31, 33, 35, 37

**Day #20:**5.2 Important Theorems Based on the Parallel Postulate**Topic:**5.2 Important Theorems Based on the Parallel Postulate**Book Section:**5.2 Important Theorems Based on the Parallel Postulate**Reference:**List of Postulates and Theorems**Class Presentations:****Katie Henry:**Solve 5.1#18**Gwen Hoshor:**Solve 5.1#30**Amira Hunter:**Solve 5.1#31 but use angle sizes 50 and 85 instead of 55 and 80.**Matthew McFarland:**Solve 5.1#32

**Exercises:**Section 5.2 # 2, 4, 8, 10, 12, 14, 16, 18, 20, 21, 22, 25, 26, 29, 31

**Day #21:**5.2 Important Theorems Based on the Parallel Postulate**(Quiz 5)****Topic:**5.2 Important Theorems Based on the Parallel Postulate**Book Section:**5.2 Important Theorems Based on the Parallel Postulate**Reference:**List of Postulates and Theorems**Class Presentations:****Brianna McFee:**(This is book exercise 5.1#33) Prove Corollary 5.2: Given lines*L*and*M*cut by a transversal*T*, if*L*and*M*are both perpendicular to*T*, then lines*L*and*M*are parallel.**Lilly Michigan:**(This is book exercise 5.1#34) Prove Corollary 5.3: Given lines*L*and*M*cut by a transversal*T*, if a pair of corresponding angles is congruent, then lines*L*and*M*are parallel.**Mitchell Myers:**(This is book exercise 5.1#35) Prove Corollary 5.4: Given lines*L*and*M*cut by a transversal*T*, if a pair of interior angles on the same side of the transversal add up to 180, then lines*L*and*M*are parallel.**Mark did this one:**Prove this statement: Given parallel lines*L*and*M*, if a line*T*intersects line*L*, then line*T*also intersects line*M*. (In your proof, you can use any postulate or theorem appearing before Corollary 5.6, which is on page 246.)**Conner Singleton:**(This is book exercise 5.1#37) Prove Corollary 5.6: Given lines parallel lines*L*and*M*, if a line*T*is perpendicular to*L*, then line*T*also perpendicular to line*M*.

**Exercises:**Section 5.2 # 2, 4, 8, 10, 12, 14, 16, 18, 20, 21, 22, 25, 26, 29, 31**Quiz 5**

**Day #22 :**5.3 Parallelograms and Rhombuses**Topic:**5.3 Parallelograms and Rhombuses**Book Section:**5.3 Parallelograms and Rhombuses**Reference:**List of Postulates and Theorems**Class Presentations:****Background:**Theorems 5.14 through 5.21 in book Section 5.3 are part of (but not all of) the following.**MEGA THEOREM****The Six Equivalent Statements Theorem : (Six Equivalent Statements about Convex Quadrilaterals)**

Given any convex quadrilateral,

the following six statements are equivalent (*TFAE*). That is, they are either all true or all false.- Both pairs of opposite sides are parallel. That is, the quadrilateral is a parallelogram.
- Both pairs of opposite sides are congruent.
- One pair of opposite sides is both congruent and parallel.
- Each pair of opposite angles is congruent.
- Either diagonal creates two congruent triangles.
- The diagonals bisect each other.

**Instructions:**- Present on the chalkboard.
- The proofs should be very short. But see me for help on Thursday if you are confused.
- Remember that in the proof of a theorem or corollary, you are allowed to use any earlier theorem or corollary. For these proofs, you are allowed to use any theorem or corollary numbered up through 5.14. You are not allowed to use Theorems 5.15 through 5.21.)

**Laura Rodgers:**Your goal is to prove that \( 2 \rightarrow 5 \).

Prove the following:

Given any convex quadrilateral \( ABCD \),

if \( \overline{AB} \cong \overline{DC} \) and \( \overline{AD} \cong \overline{BC} \)

then \( \Delta{ABD} \cong \Delta{CDB} \)**Hannah Six:**Your goal is to prove that \( 5 \rightarrow 2 \).

Prove the following:

Given any convex quadrilateral \( ABCD \),

if \( \Delta{ABD} \cong \Delta{CDB} \)

then \( \overline{AB} \cong \overline{DC} \) and \( \overline{AD} \cong \overline{BC} \)**Lindsay Stanton:**Your goal is to prove that \( 3 \rightarrow 2 \).

Prove the following:

Given any convex quadrilateral \( ABCD \),

if \( \overline{AB} \cong \overline{DC} \) and \( \overline{AB} \parallel \overline{DC} \)

then \( \overline{AD} \cong \overline{BC} \),

Hint: Draw diagonal \( \overline{BD} \). Consider parallel lines \( \overline{AB} \parallel \overline{DC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then somehow show that the two triangles that are created are congruent. Then use that to show that some segments are congruent.**Sydney Waugh:**Your goal is to prove that \( 2 \rightarrow 1 \).

Prove the following:

Given any convex quadrilateral \( ABCD \),

if \( \overline{AB} \cong \overline{DC} \) and \( \overline{AD} \cong \overline{BC} \),

then quadrilateral \( ABCD \) is a*parallelogram*. That is, \( \overline{AB} \parallel \overline{DC} \) and \( \overline{AD} \parallel \overline{BC} \)

Hint: Draw diagonal \( \overline{BD} \) and then somehow prove that the two triangles that are created are congruent. Then use that to show that some angles are congruent. Then use that to somehow show that some lines are parallel.**Tyler Wulf:**Your goal is to prove that \( 1 \rightarrow 5 \).

Prove the following:

Given any convex quadrilateral \( ABCD \),

if quadrilateral \( ABCD \) is a*parallelogram*, that is, if \( \overline{AB} \parallel \overline{DC} \) and \( \overline{AD} \parallel \overline{BC} \)

then \( \Delta{ABD} \cong \Delta{CDB} \)

Hint: Draw diagonal \( \overline{BD} \) Consider parallel lines \( \overline{AB} \parallel \overline{DC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then consider parallel lines \( \overline{AD} \parallel \overline{BC} \) and transversal \( \overline{BD} \). What can you say about some angles based on what you know about those lines? Then prove that the triangles are congruent.

**Exercises:**Section 5.3 # 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 38, 39, 41, 43

**Day #23:**5.4 Rectangles, Squares, and Trapezoids**Topic:**5.4 Rectangles, Squares, and Trapezoids**Book Section:**5.4 Rectangles, Squares, and Trapezoids**Reference:**List of Postulates and Theorems**Class Presentations:**None**Exercises:**Section 5.4 # 1, 3, 7, 8, 11, 12, 25, 26, 28, 30, 31, 32, 33, 36, 41, 44, 45

**Day #24:**6.1 Ratio and Proportion**(Quiz 6)****Topic:**6.1 Ratio and Proportion**Book Section:**6.1 Ratio and Proportion**Reference:**List of Postulates and Theorems**Class Presentations:**None**Exercises:**ection 6.1 # 12, 14, 20, 22, 24, 26, 30, 32, 34, 36, 40, 44**Quiz 6**

**Day #25:**6.2 Similar Triangles**Topic:**6.2 Similar Triangles**Book Section:**6.2 Similar Triangles**Reference:**List of Postulates and Theorems**Class Presentations:**None**Exercises:**Section 6.2 # 1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 17, 18, 19, 21, 22, 23, 24, 26, 37

**Day #26:**6.3 Applications of Similarity**Topic:**6.3 Applications of Similarity**Book Section:**6.3 Applications of Similarity**Reference:**List of Postulates and Theorems**Group Work:****Class Presentations:**None**Exercises:**Section 6.3 # 1, 3, 5, 7, 9, 11, 13, 18, 20, 24, 25, 27, 31, 33, 34, 35, 39

**Day #27:**6.4 Using Right Triangle Trigonometry to Solve Geometry Problems**(Quiz 7)****Topic:**6.4 Using Right Triangle Trigonometry to Solve Geometry Problems**Book Section:**6.4 Using Right Triangle Trigonometry to Solve Geometry Problems**Reference:**List of Postulates and Theorems**Class Presentations:****Jenna Baratie:**(6.4#34) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( b=8 \) and \( \angle B = 45^{\circ} \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.**Ashley Benedict:**(6.4#36) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( b=5 \) and \( c=7 \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.**Sam Bernstein:**(6.4#38) Triangle \( \Delta ABC \) has right angle at \( \angle C \) and sides \( a,b,c \). Given \( a=9 \) and \( \angle B = 41^{\circ} \), solve for the missing parts. Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.**Audrey Brown:**(6.4#42) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 22^{\circ} \) and \( b=9.85 \) and \( c=23.6 \), find the area of the triangle. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Dominic Buttari:**(6.4#44) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A \cong \angle B \) and \( \angle C = 48^{\circ} \) and \( c=8 \), find the area of the triangle. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Annie Dill:**(6.4#46) Trapezoid \( ABCD \) has \( \overline{AB}=16 \) and \( \overline{CD}=7 \) and \( \overline{DA}=6.4 \) and\( \angle D = 105^{\circ} \) Find the area of the trapezoid. Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.

**Exercises:**Section 6.4 # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 25, 27, 33, 35, 37, 43, 44, 45, 61, 63, 66**Quiz 7**

**Day #28:**6.5 Using Trigonometry to Solve Geometry Problems**Topic:**6.5 Using Trigonometry to Solve Geometry Problems**Book Section:**6.5 Using Trigonometry to Solve Geometry Problems**Reference:**List of Postulates and Theorems**Class Presentations:****Jessie Feilen:**(6.5#2) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 30^{\circ} \) and \( \angle C = 40^{\circ} \)and \( a=20 \), use the*Law of Sines*to find \( c \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Hanna Gerrard:**(6.5#8) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 75^{\circ} \) and \( b=20 \) and \( c=5 \), use the*Law of Sines*to find \( \angle C \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Zack Graham:**(6.5#12) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 50^{\circ} \) and \( \angle C = 60^{\circ} \)and \( c=10 \), use the*Law of Sines*to find the measures of all remaining parts of \( \Delta ABC \). Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.**Katie Henry:**(6.5#18) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle A = 80^{\circ} \) and \( b=9 \) and \( c=10 \), use the*Law of Cosines*to find \( a \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Gwen Hoshor:**(6.5#24) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( a=22 \) and \( b=21 \) and \( c=24 \), use the*Law of Cosines*to find \( \angle A \). Give an exact answer in symbols, and then a decimal approximation rounded to 3 decimal places.**Amira Hunter:**(6.5#28) Triangle \( \Delta ABC \) has sides \( a,b,c \). Given \( \angle B = 80^{\circ} \) and \( a=9 \) and \( c=11 \), use the*Law of Cosines*to find the measures of all remaining parts of \( \Delta ABC \). Give exact answers in symbols, and then decimal approximations rounded to 3 decimal places.

**Exercises:**Section 6.5 # 1, 3, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 33, 34, 35, 36, 37, 43, 45, 47**Lecture Notes:**Lecture Notes, including Class Presentation Examples

**Day #29:****In-Class Exam 3 Covering Chapters 5 - 6****Day #30:**7.1 Central Angles and Inscribed Circles**Topic:**7.1 Central Angles and Inscribed Circles**Book Section:**7.1 Central Angles and Inscribed Circles**Reference:**List of Postulates and Theorems**Class Presentations:**None**Exercises:**Section 7.1 # 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 48, 48, 51, 52

**Day #31:**7.2 Chords of a Circle**Topic:**7.2 Chords of a Circle**Book Section:**7.2 Chords of a Circle**Reference:**List of Postulates and Theorems**Class Presentations:****Laura Rodgers:**Present a solution to problem 7.2#4 on the chalkboard.**Brianna McFee:**Present a solution to problem 7.2#12 on the chalkboard. Try to not use Theorem 7.8. Rather, use the general strategy of identifying similar triangles in the figure, and then using the ratios that you get from having similar triangles. That is,- Identify two triangles that you know are similar. Draw them with corrseponding orientation and all known quantities labeled.
- Write down the ratios that you get from knowing that the triangles are similar.

**Mitchell Myers:**Present a solution to problem 7.2#16 on the chalkboard.

**Exercises:**Section 7.2 # 1, 3, 5, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 28, 32, 33, 34, 36, 37, 38, 43, 46

**Monday is Veterans Day Holiday: No Class****Day #32:**7.3 Secants and Tangents**(Quiz 8)****Topic:**7.3 Secants and Tangents**Book Section:**7.3 Secants and Tangents**Reference:**List of Postulates and Theorems**Class Presentations:****Lilly Michigan:**Present a solution to problem 7.3#6 on the chalkboard. Give an exact answer first and then a decimal approximation. Try to not use a theorem that tells you about the lengths of the segments. Rather, use the general strategy of identifying similar triangles in the figure, and then using the ratios that you get from having similar triangles. That is,- Identify two triangles that you know are similar. Draw them with corrseponding orientation and all known quantities labeled.
- Write down the ratios that you get from knowing that the triangles are similar.

**Conner Singleton:**Present a solution to problem 7.3#12 on the chalkboard.**Hannah Six:**Present a solution to problem 7.3#25 on the chalkboard.

**Exercises:**Section 7.3 # 1, 3, 5, 11, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 38, 39**Quiz 8**

**Day #33:**7.3 Secants and Tangents**Topic:**7.3 Secants and Tangents**Book Section:**7.3 Secants and Tangents**Reference:**List of Postulates and Theorems**Class Presentations:****Lindsay Stanton:**Problem 7.3#31 Prove Corollary 7.15: If two tangent lines are drawn to a circle from the same point in the exterior of the circle, then the distances from the common point to the points of tangency are equal.**Sydney Waugh:**Problem 7.3#32 Prove that if a tangent line and a secant line are parallel, then the arcs that they intercept are congruent.**Tyler Wulf:**Prove that if line \( L \) is perpendicular to segment \( \overline{CB} \) at point \( B \), then line \( L \) is*tangent*to the circle that is centered at \( C \) and passes through \( B \). That is, line \( L \) only touches the circle once, at point \( B \).

**Exercises:**Section 7.3 # 1, 3, 5, 11, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 38, 39

**Day #34:**8.1 Coordinates and Distance in the Plane**(Quiz 9)****Topic:**8.1 Coordinates and Distance in the Plane**Book Section:**8.1 Coordinates and Distance in the Plane**Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)****Jenna Baratie:**8.1 # 10 about distance formula with variable**Ashley Benedict:**8.1 #8 about collinearity test. (Refer to Theorem 8.2) Don’t take time or chalkboard space to show the distance calculations. Just show the results of those calculations and your conclusions.**Sam Bernstein:**8.1 # 18 about testing triangles to see if they are right triangles. Your tools should be:- Theorem 4.4 The Converse of the Pythagorean Theorem: If \( a^2 + b^2 = c^2 \), then angle \( \angle C \) is a right angle.
- Theorem 3.8 The Pythagorean Theorem (The contrapositive Version) If \( a^2 + b^2 \neq c^2 \), then angle \( \angle C \)is not a right angle.

**Exercises:**Section 8.1 # 5, 6, 7, 9, 13, 17, 19, 20, 21, 23, 27**Quiz 9**

**Day #35:**8.2 Slope and Starting Section 8.3 Equations of Lines and Circles**Topic:**8.2 Slope and Equations of Lines from Section 8.3**Book Section:**8.2 Slope and 8.3 Equations of Lines**Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)****Audrey Brown:**(Example similar to 8.2 # 27) Find the value of \( a \) so that slope of line segment having endpoints \( (-11,4) \) and \( (a,-3) \) is \( -1/4 \).**Dominic Buttari:**(8.2 # 24) Find the slope of a line perpendicular to line \( \overleftrightarrow{AB} \) where- \( A=(0,4) \) and \( B=(-6,-5) \)
- \( A=(-1,5) \) and \( B=(-1,3) \)

**Annie Dill:**(8.2 # 28) Find the value of \( b \) so that the line segment having endpoints \( (5,1) \) and \( (-6,b) \) is perpendicular to the segment having endpoints \( (1,4) \) and \( (-1,0) \).**Jessie Feilen:**(8.2 # 29) One diagonal of rhombus \( ABCD \) has vertices \( A=(9,-3) \) and \( C=(6,1) \). Find the slope of the other diagonal.**Hanna Gerrard:**(8.3 #24) Find the equations of the perpendicualr bisectors of the sides of the triangle whose vertices are \( (0,0),(4,0),(0,3) \).**Zack Graham:**(8.3#26) Find the equation of the altitude line that passes through point \( P \) of triangle \( \Delta PRS \) with vertices \( P=(3,5),R=(-1,1),S=(7,-3) \).**Katie Henry:**(8.3 #28c) Use the substitution method to find the simultaneous solution of the system of equations. (Show the steps)- \( 2x-4y=7 \)
- \( 5x+y=1 \)

**Exercises:**- Section 8.2 # 11, 13, 17, 23, 27, 28, 29, 35
- Section 8.3 # 1, 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 37, 39, 41, 43, 45

**Day #36:**8.3 Equations of Lines and Circles**Topic:**8.3 Equations of Lines and Circles**Book Section:**8.3 Equations of Lines and Circles**Class Presentations: (Class Presentation CP6. I will keep your best 5 of 6 class presentations and drop the lowest one.)****Lilly Michigan:**(8.3#38) Identify the center and radius of each circle whose equation is given.- \( (x-2)^2+(y+5)^2=64 \)
- \( (x+3)^2+(y-4)^2=20 \)

**Gwen Hoshor:**(8.3#40) Write an equation of the circle satisfying each of the following conditions.- Center \( (3,-4) \) and passing through \( (2,-6) \)
- Center \( (-2,5) \) and radius \( 7 \)
- Endpoints of a diameter at \( (-4,5) \) and \( (12,7) \)

**Amira Hunter:**(8.3#41) Find the coordinates of the*centroid*of the triangle with vertices \( A=(-5,-1), B=(3,3), C=(5,-5)\). (Hint: It is a fact proven in MATH 3110 that in any given triangle, the three*medians*of the triangle intersect in a common point. This point is called the*centroid*. To find the centroid, one must find the line equations for two of the three median lines, and then use those line equations to determine the point of intersection of those two median lines. The third median line is guaranteed to also pass through this point, so you don't need to find the third median line. See the book page 454, the boxed [Solution of Applied Problem] to see an example of the calculation of the coordinates of the centroid of a triangle.)**Brianna McFee:**(8.3#44) Find the coordinates of the*circumscribing circle*of the triangle with vertices \( A=(4,5), B=(8,-3), C=(-4,-3)\). (Hint: It is a fact that any three*non-collinear*points lie on exactly one common circle. That means that given any triangle, there exists exactly one circle that passes through the three vertices of the triangle. One says that this circle*circumscribes the triangle.*. Your goal is to find the equation for this circle. The strategy is to- Find the point
*P*that is the center of the circle. - Find the radius of the circle
- Use the known center and radius to build the equation of the circle.

*P*will have the property that \( PA=PB=PC \), because those are the lengths of radial segments. Now consider the equation \( PA=PB \). It tells us that point*P*is equidistant from points*A*and*B*. But then Theorem 4.10, the*Perpendicular Bisector Theorem*, tells us that point*P*must lie on the*perpendicular bisector*of segment \( \overline{AB} \). Similarly, the equation \( PB=PC \) tells us that point*P*is equidistant from points*B*and*C*, and so point*P*must*also*lie on the*perpendicular bisector*of segment \( \overline{BC} \). So to find the coordinates of point*P*, start by finding the line equations for the*perpendicular bisector*of segment \( \overline{AB} \) and for the*perpendicular bisector*of segment \( \overline{BC} \). Then use those line equations to determine the point of intersection of those two perpendicular bisectors. This point will be*P*. Once you have point*P*, you should be able to compute the circle's radius and build the equation for the circle.)- Find the point

**Exercises:**Section 8.3 # 1, 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 37, 39, 41, 43, 45

**Day #37:****In-Class Exam 4 Covering Chapters 7 - 8****Wednesday through Friday is Thanksgiving Break: No Class**

**Day #38:**9.1 Isometries and Congruence**Topic:**9.1 Isometries and Congruence**Book Section:**9.1 Isometries and Congruence**Mitchell Myers:**Present your solutions on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some: Graph Paper.- Problem 9.1#6a
- Problem 9.1#6b
- Problem 9.1#12c

**Laura Rodgers:**- Part 1: Give the coordinates of the images of the following points under the rotation of \( 90^\circ \) around the origin. (Present your solutions on paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:
*Graph Paper*).- \( (3,-1) \) (Illustrate on
*graph paper*.) - \( (-6,-3) \) (Illustrate on
*graph paper*.) - \( (-4,2) \) (Illustrate on
*graph paper*.) - \( (x,y) \) (Illustrate on
*blank paper*.)

- \( (3,-1) \) (Illustrate on
- Part 2: We would express the results of the rotation of \( 90^\circ \) around the origin, applied to the point \( (4,2) \), in the following way:

*The point \( (4,2) \) rotates \( 90^\circ \) around the origin to the point \( (-2,4) \).*

Write sentences that describe the result of the following rotations, and draw a clear picture on blank paper to illustrate each. (One picture per sheet.)- the rotation of \( 180^\circ \) around the origin, applied to the point \( (x,y) \)
- the rotation of \( 270^\circ \) around the origin, applied to the point \( (x,y) \)
- the rotation of \( 360^\circ \) around the origin, applied to the point \( (x,y) \)

- Part 1: Give the coordinates of the images of the following points under the rotation of \( 90^\circ \) around the origin. (Present your solutions on paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some:
**Conner Singleton:**(Problem 9.1#36)- Draw \( \Delta ABC \) with \( A=(3,1), B=(4,3), C=(5,-2) \), and draw its image under the reflection with respect to the line \( y=x \) (Illustrate on
*graph paper*. Be sure to draw the line \( y=x \) and to label all important points with their \( (x,y) \) coordinates.) - If a point \( P=(a,b) \) is reflected across the line \( y=x \), what are the coordinates of the resulting point \( P' \)? (Illustrate on blank paper. Be sure to draw the line \( y=x \) and to label all important points with their \( (x,y) \) coordinates.)

- Draw \( \Delta ABC \) with \( A=(3,1), B=(4,3), C=(5,-2) \), and draw its image under the reflection with respect to the line \( y=x \) (Illustrate on
**Hannah Six:**(9.1#44) Print out the drawing at the following link:*9.1#44 Drawing*. Use a ruler to draw the reflection line that takes \( \Delta ABC \) to \( \Delta A'B'C' \).

**Exercises:**Section 9.1 # 3, 5, 11, 12, 13, 15, 25, 26, 35, 36, 39, 40, 41, 43, 45, 47, 48

**Day #39:**9.3 Problem Solving Using Transformations**(Quiz 10)****Topic:**9.1 Isometries and Congruence**Book Section:**9.1 Isometries and Congruence**Lindsay Stanton:**(Present your solution on graph paper, large and clear. If you need graph paper, go to the following link and print some: Graph Paper.) Let triangle \( \Delta ABC \) have vertices \( A=(4,8), B=(7,1), C=(12,3) \) and let triangle \( \Delta DEF \) have vertices \( A=(16,18), B=(19,11), C=(224,13) \). Let \( L \) be the line \( y=10 \) and let \( M \) be the line \( y=20 \). Reflect \( \Delta ABC \) and \( \Delta DEF \) across line \( L \) to get triangles \( \Delta A'B'C' \) and \( \Delta D'E'F' \). Then reflect \( \Delta A'B'C' \) and \( \Delta D'E'F' \) across line \( M \) to get triangles \( \Delta A''B''C'' \) and \( \Delta D''E''F'' \). Draw all six triangles.**Sydney Waugh:**(Present your solutions on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some: Graph Paper.) Let \( L \) be the line \( y=0 \) and let \( M \) be the line \( y=x \).- Let triangle \( \Delta ABC \) have vertices \( A=(5,-8), B=(10,-8), C=(11,-5) \). Reflect \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \). Then reflect \( \Delta A'B'C' \) across line \( M \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
- (Start over on a new sheet of graph paper.) Let triangle \( \Delta ABC \) have vertices \( A=(5,2), B=(10,2), C=(11,5) \). Reflect \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \). Then reflect \( \Delta A'B'C' \) across line \( M \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.

**Tyler Wulf:**(Present your solution on graph paper, large and clear, one problem per sheet. If you need graph paper, go to the following link and print some: Graph Paper.) Let triangle \( \Delta ABC \) have vertices \( A=(5,2), B=(10,2), C=(11,5) \). Let \( L \) be the line \( y=x \).- Translate \( \Delta ABC \) 10 units to the right to get triangle \( \Delta A'B'C' \) and then reflect triangle \( \Delta A'B'C' \) across line \( L \) to get triangle \( \Delta A''B''C'' \). Draw all three triangles.
- (Start over on a new sheet of graph paper.) Reflect triangle \( \Delta ABC \) across line \( L \) to get triangle \( \Delta A'B'C' \) and then translate triangle \( \Delta A'B'C' \) 10 units to the right to get triangle \( \Delta A''B''C'' \). Draw all three triangles.

**Exercises:**Section 9.3 # 1, 3, 4, 5, 7, 8, 25**Quiz 10**

**Day #40:**Leftovers and Course Review**Topic:**Leftovers and Course Review**Book Section:**The whole book!**Class Presentations:**None!**Exercises:**None!

**Day #41: Fri Dec 13**- The final Exam is on Friday, December 13, 2019 in Morton 223.
- The exam starts after 8:00am, as soon as all your stuff is put away
- The exam ends at 10:00am, no exceptions
**Bring your Theorem List and your Calculator.**- No books, no cell phones.
- The Exam is 10 problems
**Problem about recognizing a pattern and finding a formula for it**- 1.2 # 5, 7, 9, 19, 27, 29, 33

**Problem about angle measure**- 2.3 # 9, 10, 13, 15, 19
- 5.1 # 29, 31, 32
- 5.2 # 21, 22
- 5.3 # 13, 15, 31

**Problem about area, surface area, or volume**- 3.1 # 11, 13, 19, 20, 35, 37, 38
- 3.2 # 14, 16, 17, 18, 19, 21, 22, 23
- 3.4 # 8, 12, 15, 17, 20, 22, 27, 28
- 3.5 # 7, 8, 13, 22, 23
- 5.3 # 33

**Problem involving introducing a variable**- 2.1 # 17, 19
- 3.1 # 17
- 3.4 # 16
- 8.1 # 9
- 8.2 # 28

**A proof**- 4.2 # 40, 42
- 4.3 # 9, 11, 13, 15, 16, 18
- 5.2 # 25, 26, 29
- 5.3 # 37
- 7.2 # 33, 37, 38
- 7.3 # 31, 33

**Problem involving similarity**- 6.2 # 5, 7, 9, 10, 11, 12
- 6.3 # 1, 3, 5, 7, 9, 11, 24, 25

**Problem involving trigonometry**- 6.4 # 42, 43, 44, 45, 56
- 6.5 # 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 33, 34, 35, 36, 37

**Problem about circle angles, secants, tangents**- 7.1 # 37, 43, 49, 51
- 7.2 # 3, 11, 15
- 7.3 # 1, 14, 26, 39

**Problem about distance, slope**- 8.1 # 9, 13, 17
- 8.2 # 23, 28, 31
- 8.3 # 23

**Problem about isometries**- 9.1 # 11, 25, 26, 36, 40, 43 (using ruler, not compass & straightedge), 47, 48
- 9.3 # 1, 3, 4, 5, 7, 8

**Grading: **

During the semester, you will accumulate a * Points Total* of up to

**Class Presentations:**5 presentations @ 20 points each = 100 points possible**Quizzes:**Best 8 of 10 quizzes @ 25 points each = 200 points possible**In-Class Exams:**Best 3 of 4 exams @ 150 points each = 450 points possible**Final Exam:**250 points possible

At the end of the semester, your * Points Total* will be converted into your

- 900 - 1000 points = 90% - 100% = A-, A = You mastered all concepts, with no significant gaps.
- 800 - 899 points = 80% - 89.9% = B-, B, B+ = You mastered all essential concepts and many advanced concepts, but have some significant gaps.
- 700 - 799 points = 70% - 79.9% = C-, C, C+ = You mastered most essential concepts and some advanced concepts, but have many significant gaps.
- 600 - 699 points = 60% - 69.9% = D-, D, D+ = You mastered some essential concepts.
- 0 - 599 points = 0% - 59.9% = F = You did not master essential concepts..

**There is no curve.**

**Throughout the semester, your current scores and current course grade will be available in an online gradebook on the Blackboard system.**

**Course Structure: **

One learns math primarily by trying to solve problems. This course is designed to provide structure for you as you learn to solve problems, and to test how well you have learned to solve them. This structure is provided in the following ways.

**Exercises:**The centerpiece of this course is the list of*Exercises*, found farther down this web page. The goal of the course is for you to be able to solve the exercises in this table. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study.**The quizzes and exams will be made up of problems similar to suggested exercises.****Reading:**To succeed in the course, you will need to read the textbook, study the examples in it. Many of the examples are exactly like exercises on your exercise list. And you will need to read the textbook in order to understand how to do your Presentation Assignments**Office Hours:**Come to my office hours for help on your Presentation Assignments and Exercises**Lectures:**In lecture, I will sometimes highlight textbook material that is particularly important, sometimes present material in a manner different from the presentation in the book, and sometimes solve sample problems. We have 36 lectures, totaling 1980 minutes. It is not possible to cover the entire content of the course in 1980 minutes, and the lectures are not meant to do that. Lectures are meant to be a supplement to your reading the textbook and solving problems.**Tutoring:**Free tutoring is available in the Morton Math Tutoring Lab, in the Math Library, Morton 415a. Make use of it!**Class Presentations:**Each of you will be called upon to do five*Class Presentations*during the semester. After the first week of class, you will always receive your assignment at least a week before you have to make your presentation. (The Class Presentation Assignments are posted in the Calendar above.) The presentations will involve you presenting a basic example during lecture. The basic examples are always about*new material that we will be covering in class that day*. To prepare for these Class Presentations, you will need to read the textbook and study its examples. If you are confused about your Class Presentation Assignment, you are welcome to come to my office hours to discuss it. However, before coming to me for help, you need to be sure and read the book and study its examples, and do some work on the assignment. I will not discuss your assignment with you if you have not studied the book.**Quizzes and Exams:**The quizzes and exams are based on the list of*Exercises*, found farther down this web page.

**Exercises: **

One learns math primarily by trying to solve problems. The centerpiece of this course is the list of Exercises found in the table below. The goal of the course is for you to be able to solve the exercises in this table. These exercises are not to be turned in and are not graded, but you should do as many of them as possible and keep your solutions in a notebook for study. **The quizzes and exams will be made up of problems similar to suggested exercises.**

**On all problems: Find an exact answer in symbols first, then find a decimal approximation if one is called for. That is, "EAFTDA".**

- Section 1.1 Problem Solving Strategies # 3, 5, 7, 11, 17, 19, 23, 25, 33, 39
- Section 1.2 More Problem Solving Strategies # 5, 7, 9, 15, 19, 21, 23, 25, 27, 29, 33, 35, 37, 39, 41
- Section 2.1 Undefined Terms, Definitions, Postulates # 7, 11, 15, 17, 19, 21, 22, 39, 42
- Section 2.2 Polygons and Circles # 3, 5, 7, 11, 15, 19, 21, 27, 29, 31, 33, 35
- Section 2.3 Angle Measure in Polygons and Tessalations # 1, 3, 9, 13, 15, 19, 21, 23, 25, 33
- Section 2.4 Three-Dimensional Shapes # 1, 3, 5, 9, 11, 15, 17, 19, 21, 23, 25, 27, 29, 33, 35, 37
- Section 2.5 Dimensional Analysis # 5, 7, 9, 11, 13, 17, 19, 23, 25, 27
- Section 3.1 Perimeter, Circumference, Area of Basic Shapes # 5, 7, 11, 13, 17, 19, 20, 27, 28, 31, 33, 35, 37, 38, 51
- Section 3.2 More Area Formulas # 1, 9, 13, 14, 16, 17, 18, 19, 21, 22, 23, 36, 39, 43
- Section 3.3 Pythagorean Theorem & Right Triangles # 2, 4, 9, 12, 13, 14, 22, 23, 24, 25, 30, 35, 48, 49
- Section 3.4 Surface Area # 3, 8, 12, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29 (
*EAFTDA*) - Section 3.5 Volume # 3, 7, 13, 17, 22, 23, 28, 41, 43, 44, 45, 46 (
*EAFTDA*) - Section 4.1 Reasoning and Proof in Geometry # 17, 18, 19, 20, 22, 25, 26, 27, 8, 29, 30, 31, 32, 37, 38, 39, 40, 41, 42, 45
- Section 4.2 Triangle Congruence Conditions # 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 24, 25, 26, 35, 37, 40, 42
- Section 4.3 Problem Solving Using Triangle Congruence # 3, 5, 7, 9, 11, 12, 13, 15, 16, 17, 18, 19, 20
- Section 5.1 Indirect Reasoning and the Parallel Postulate # 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 17, 29, 31, 33, 35, 37
- Section 5.2 Important Theorems Based on the Parallel Postulate # 2, 4, 8, 10, 12, 14, 16, 18, 20, 21, 22, 25, 26, 29, 31
- Section 5.3 Parallelograms and Rhombuses # 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 38, 39, 41, 43
- Section 5.4 Rectangles, Squares, and Trapezoids # 1, 3, 7, 8, 11, 12, 25, 26, 28, 30, 31, 32, 33, 36, 41, 44, 45
- Section 6.1 Ratio and Proportion # 12, 14, 20, 22, 24, 26, 30, 32, 34, 36, 40, 44
- Section 6.2 Similar Triangles # 1, 2, 3, 5, 7, 9, 10, 11, 12, 13, 17, 18, 19, 21, 22, 23, 24, 26, 37
- Section 6.3 Applications of Similarity # 1, 3, 5, 7, 9, 11, 13, 18, 20, 24, 25, 27, 31, 33, 34, 35, 39
- Section 6.4 Using Right Angle Trig to Solve Geom Problems # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 25, 27, 33, 35, 37, 43, 44, 45, 61, 63, 66
- Section 6.5 Using Trigonometry to Solve Geometry Problems # 1, 3, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 33, 34, 35, 36, 37, 43, 45, 47
- Section 7.1 Central Angles and Inscribed Angles # 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 48, 48, 51, 52
- Section 7.2 Chords of a Circle # 1, 3, 5, 7, 11, 13, 15, 19, 21, 23, 24, 25, 27, 28, 32, 33, 34, 36, 37, 38, 43, 46
- Section 7.3 Secants and Tangents # 1, 3, 5, 11, 14, 15, 17, 19, 21, 23, 25, 26, 27, 29, 31, 32, 33, 34, 35, 38, 39
- Section 8.1 Coordinates and Distance in the Plane # 5, 6, 7, 9, 13, 17, 19, 20, 21, 23, 27
- Section 8.2 Slope # 11, 13, 17, 23, 27, 28, 29, 35
- Section 8.3 Equations of Lines and Circles # 1, 3, 5, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 37, 39, 41, 43, 45
- Section 9.1 Isometries and Congruence # 3, 5, 11, 12, 13, 15, 25, 26, 35, 36, 39, 40, 41, 43, 45, 47, 48
- Section 9.3 Problem Solving Using Transformations # 1, 3, 4, 5, 7, 8, 25

**Attendance Policy: **

Attendance is required for all lectures and exams, and will be recorded using sign-in sheets and traditional roll call.

**Missing Class: **If you miss a class for any reason, it is your responsibility to copy someone's notes or download my notes from the course web page, and study them. I will not use office hours to teach topics discussed in class to students who were absent.

**Missing a Quiz or Exam Because of Illness: **If you are too sick to take a quiz or exam, then you must

- send me an e-mail before the quiz/exam, telling me that you are going to miss it because of illness, then
- then go to the Hudson Student Health Center.
- Later, you will need to bring me documentation from Hudson showing that you were treated there.

**Missing Quizzes or Exams Because of University Activity: **If you have a University Activity that conflicts with one of our quizzes or exams, you must contact me before the quiz or exam to discuss arrangements for a make-up. I will need to see documentation of your activity. If you miss a quiz or an exam because of a University Activity without notifying me in advance, you will not be given a make-up.

**Missing Quizzes or Exams Because of Personal Travel Plans: **Many of our quizzes and in-class exams are on Fridays or Mondays. We have an exam on Monday, November 25th. Students often ask me if they can make take a quiz or exam early or late because they have plans to miss a Friday or Monday class in order to lengthen a weekend or a holiday. The answer is always, *No you may not take the quiz or exam early or late. You will just have to change your travel plans or forfeit that quiz or exam.*

**Policy on Cheating: **

If cheat on a quiz or exam, you will receive a zero on that quiz or exam and I will submit a report to the Office of Community Standards and Student Responsibility (OCSSR).

If you cheat on another quiz or exam, you will receive a grade of F in the course and I will again submit a report to the OCSSR.

**Calculators and Free Online Math Resources: **

**Calculators:**

Calculators will not be allowed on quizzes or exams.

**Websites with Useful Math Resources: **

In lectures, I often use a computer for graphing and calculating. The computer tools that I use are free online resources that are easily accessible at the following link.

Link to Free Online Math Resources

I use the same online resources in my office, instead of a calculator. You are encouraged to use these same free resources at home, instead of a calculator.

page maintained by Mark Barsamian, last updated Dec 6, 2019