2017 - 2018 Fall Semseter
MATH 2110 Introductory Geometry for Middle School Teachers (Barsamian)
Class Presentation Topics

Each of you will be called upon to make class presentations ten times during the semester. Sometimes these presentations will be about introducing a new concept to the class. Other times, the presentations will involve presenting an example that illustrates a new concept. They will always involve new concepts, which means that to prepare for them, you will need to learn material that has not yet been presented in class. You will always receive your presentation assignment at least a week before you have to make the presentation, and you are welcome to come and discuss your assignment with me in the week before your presentation. Each assignment is worth 10 points, with the points given according to the usual 90,80,70,60 scale. Please note that the Class Presentation assignments cannot be made-up in the case of absence, even excused absence, because they involve participation in a class discussion.

The daily assignments are listed below.

Wed Aug 30 (Meeting Number 2) Section 1.2

• Benedict (CP01): Present solutions to book exercises 1.2 # 2,4,6
• Bown (CP01): Present solutions to book exercises 1.2 # 18,19

Fri Sep 1 (Meeting Number 3) Section 2.1

• Chapman (CP01): Present solutions to book exercises 2.1 # 16,18
• Coleman (CP01): Present a solution to book exercise 2.1 # 22

Wed Sep 6 (Meeting Number 4) Section 2.2

• Murawski (CP01): Present solutions to book exercises 2.2 # 28
• Rush (CP01): Present solutions to book exercises 2.2 # 30

Fri Sep 8 (Meeting Number 5) Section 2.3

• Graham (CP01): Present solutions to book exercises 2.2 # 8,20
• Schwieterman (CP01): Present solutions to book exercises 2.2 # 36
• Silveira (CP01): Present a solution to book exercise 2.3 # 4
• Sullivan (CP01): Present a solution to book exercise 2.3 # 33, but not using the pattern from the back of the book.

Mon Sep 11 (Meeting Number 6) Section 2.4

• Benedict (CP02): Present a solution to book exercise 2.4 # 6
• Bown (CP02): Present a solution to book exercise 2.4 # 28

Wed Sep 13 (Meeting Number 7) Section 2.5

• Chapman (CP02): Present a solution to book exercise 2.5 # 22. Present the conversion as a single line equation.
• Coleman (CP02): Present a solution to book exercise 2.5 # 18. Present the conversion as a single line equation.
• Graham (CP02): Present a solution to book exercise 2.5 # 23. Present the conversion as a single line equation.
• Murawski (CP02): Present a solution to book Section 2.5 Review Exercise #2 (page 99). Present the conversion as a single line equation.
• Rush (CP02): Present a solution to book Section 2.5 Review Exercise #4 (page 99). Present the conversion as a single line equation.
• Schwieterman (CP02): Present a solution to book Section 2.5 Review Exercise #5 (page 99). Present the conversion as a single line equation.
• Silveira (CP02): Present a solution to book Chapter 2 Test Problem #21 (page 100). Present the conversion as a single line equation.
• Sullivan (CP02): Present a solution to book Chapter 2 Test Problem #23 (page 101). Present the conversion as a single line equation.

Mon Sep 18 (Meeting Number 9) Section 3.1

• Benedict (CP03): (Exercise similar to 3.1 # 17) The length of a rectangle is 6 less than twice its width. If the perimeter of the rectangle is 96 inches, find the dimensions of the rectangle.
• Bown (CP03): (Exercise 3.1 # 18) The width of a rectangle is 18 less than length. If the area of the rectangle is 1440 square inches, find the dimensions of the rectangle.
• Chapman (CP03): Present a solution to 3.1 # 53 (a), and then explain what is happening.

Wed Sep 20 (Meeting Number 10) Section 3.2

• Coleman (CP03): Present a solution to 3.2 # 14
• Graham (CP03): Present a solution to 3.2 # 16, 20
• Murawski (CP03): Present solutions to 3.2 # 18, 19

Fri Sep 22 (Meeting Number 11) Section 3.3

• Rush (CP03): Present a solution to 3.3 # 29
• Schwieterman (CP03): 3.3 # 54, but you only need to find one geometric proof that is different from those presented in Section 3.3 and in exercises 3.3 # 29, 30.

Mon Sep 25 (Meeting Number 12) Section 3.4

• Silveira (CP03): Present a solution to 3.4 # 16. Give an exact answer in symbols, not a rounded answer.
• Sullivan (CP03): Present a solution to 3.4 # 29. Instead of dimensions 1.25 and 1.86 shown in the picture, use numbers 4 and 7. Give an exact answer in symbols, not an approximate answer.

Wed Sep 27 (Meeting Number 13) Section 3.5

• Benedict (CP04): Present a solution to 3.5 # 45 about volume of concrete and amount of carpet needed for steps, but use tread width, height, and depth of W, H, and D instead of 80, 25, and 20.
• Bown (CP04): Present a solution to 3.5 # 41 about volume of rubber in a tennis ball but use circumference C cm and thickness T cm instead of 22 cm and 0.6 cm.
• Chapman (CP04): Present a solution 3.5 # 43 about pumping liquid out of spherical tank, but use diameter D ft instead of 6 ft and liquid volume G gallons instead of 200 gallons.

Fri Sep 29 (Meeting Number 14) Section 4.1

• Coleman (CP04): Give an example of a conditional statement S such that S is true but the converse of S is false.
• Graham (CP04): Give an example of a conditional statement S such that S is true and the converse of S is also true.
• Murawski (CP04): Give an example of a conditional statement S such that S is false but the converse of S is true.
• Rush (CP04): Give an example of a conditional statement S such that S is false and the converse of S is also false.

Mon Oct 2 (Meeting Number 15) Section 4.2

• Schwieterman (CP04): Solve 4.2 # 10, 14
• Silveira (CP04): Solve 4.2 # 40.
• Sullivan (CP04): Solve 4.2 # 42.

Wed Oct 11 (Meeting Number 19) Section 5.1

• Benedict (CP05): Solve 5.1 # 30
• Bown (CP05): Solve 5.1 # 32
• Chapman (CP05): Solve 5.1 # 10

Fri Oct 13 (Meeting Number 20) Section 5.2

• Coleman (CP05): Solve 5.2 # 26

Mon Oct 16 (Meeting Number 21) Section 5.2

• Graham (CP05): Solve 5.2 # 29
• Murawski (CP05): Solve 5.2 # 22

Wed Oct 18 (Meeting Number 22) Section 5.3

• Rush (CP05): What is the definition of a parallelogram? (Find it in the reading.)
• Schwieterman (CP05): The book says in Corollary 5.15 that in a parallelogram, the opposite sides are congruent and the opposite angles are congruent. Where does that come from?
• Silveira (CP05): Solve 5.3 # 13

Fri Oct 20 (Meeting Number 23) Section 5.4

• Chapman (CP06): I would like you to do a translation exercise. (You don't have to actually prove anything!) Each of the exercises 5.4 # 39, 40, 41, 42, 43 says to prove some statement. But the statements are worded in a way that is not so helpful for setting up a proof. It would be more helpful if the statements were worded as conditional statements. For each of the five exercises, translate the statement to be proven into a new statement that is a conditional statement, "If P then Q." For starters, you can look at the book's presentationm of Theorem 5.27, on page 271. That will actually give you one of the translations that you need. But beware: some of the five exercises that I have assigned to you are worded in a way that is misleading, that makes the translation tricky. (That's why I assigned this as a Class Presentation.)
• Coleman (CP06): Exercise 5.4 # 44. Hint: Try to solve 5.4 # 45 first, and study the book's solution for that exercise. Then try to use the same technique for # 44.

Mon Oct 23 (Meeting Number 24) Section 6.1

• Sullivan (CP05): 6.1 # 20
• Benedict (CP06): 6.1 # 34

Wed Oct 25 (Meeting Number 25) Section 6.2

• Bown (CP06): 6.1 # 40, 44

Fri Oct 27 (Meeting Number 26) Section 6.3

• Chapman (CP07): 6.2 # 10 about a triangle cut by a line parallel to the triangle's base.
• Coleman (CP07): 6.2 # 12 about nested similar triangles
• Graham (CP06): 6.2 # 19 with modifications:
  1. (This is 6.2 # 19) Prove that if trapezoid ABCD is isosceles, then triangle AED ~ triangle CEB.
  2. If trapezoid ABCD is isosceles, what is the relationship between triangle AEB and triangle CED?
  3. If trapezoid ABCD is not isosceles, what is the relationship between triangle AED and triangle CEB?
  4. If trapezoid ABCD is not isosceles, what is the relationship between triangle AEB and triangle CED?
• Murawski (CP06): 6.3 # 2 about similar triangles created by the altitude to hypotenuse of a right triangle
• Rush (CP06): 6.3 # 4 about similar triangles created by the altitude to hypotenuse of a right triangle
• Schwieterman (CP06): 6.3 # 6 about similar triangles created by the altitude to hypotenuse of a right triangle

Mon Oct 30 (Meeting Number 27) Section 6.4

• Silveira (CP06): 6.4 # 42 (Give an exact answer, in symbols, then give a decimal approximation, rounded to the nearest tenth.)
• Sullivan (CP06): 6.4 # 46 (Give an exact answer, in symbols, then give a decimal approximation, rounded to the nearest tenth.)

Wed Nov 8 (Meeting Number 31) Section 7.2

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

• Bown (CP07): 7.1 # 43 about side length for inscribed quadrilateral
• Chapman (CP08): 7.2 # 11 involving lengths of segments formed by intersecting chords

Mon Nov 13(Meeting Number 32) Section 7.3

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

• Coleman (CP08): 7.2 # 32 prove that in a circle, parallel lines intercept congruent arcs
• Graham (CP07): 7.2 # 33 prove that in the same or congruent circles, congruent chords are equidistant from the center
• Murawski (CP07): 7.3 # 3 about measures of segments that are part of secant lines that intersect outside a circle

Wed Nov 15 (Meeting Number 33) Section 7.3

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

• Silveira (CP07): 7.3 # 29 about areas of regions formed by circles and a square
• Bown (CP08): 7.3 # 32 prove that if a tangent and secant line are parallel, they intercept congruent arcs

Fri Nov 17 (Meeting Number 34) Section 8.1

Remember to streamline your presentations. The individual steps of basic calculations don't need to be written on the board. Instead, write what calculation was done, and give the result. Only show details of calculations if they are particularly tricky or surprising.

• Rush (CP07): 7.3 # 14 about angles formed by tangent and secant lines
• Graham (CP08): 8.1 # 18 about testing triangles to see if they are right triangles
• Schwieterman (CP07): 7.3 # 26 about length of segments formed by a triangle and its inscribed circle

Mon Nov 20 (Meeting Number 35) Section 8.2

Presentation Assignments (Remember to streamline your presentations. The individual steps of basic calculations don't need to be written on the board. Instead, write what calculation was done, and give the result. Only show details of calculations if they are particularly tricky or surprising.)

• Chapman (CP09): 8.1 #8 about collinearity test
• Coleman (CP09): 8.1 # 10 about distance formula with variable
• Murawski (CP08): 8.2 # 24 Give slope of a line perp to AB where (a) A=(0,4), B=(-6,-5) and (b) A=(-1,5),B=(-1,3)
• Rush (CP08): 8.2 # 28 Find b so that slope of segment having endpoints (5,1) and (-6,b) is perpendicular to segment having endpoints (1,4) and (-1,0)
• Schwieterman (CP08): 8.2 # 29 One diagonal of rhombus ABCD has vertices A(9,-3) and C(6,1) Find slope of the other diagonal.

Quiz 9 will be one of these problems from Section 7.3. Also, one of these problems will be on Exam 4, so there is a double incentive to study these problems.

• 7.3 # 5, 11, 15, 17, 19, 21, 23, 25, 27, 31, 33, 38, 39

Wed Nov 29 (Meeting Number 37) Section 8.3

Presentation Assignments (Remember to streamline your presentations. The individual steps of basic calculations don't need to be written on the board. Instead, write what calculation was done, and give the result. Only show details of calculations if they are particularly tricky or surprising.)

• Silveira (CP08): 8.3 # 40 Write the equation of a circle with certain specifications.
• Bown (CP09): Explain what the Orthocenter of a triangle is. Then solve 8.3 # 42 about finding the orthocenter of a triangle.
• Chapman (CP10): Explain what the Circumcenter of a triangle is. Then solve 8.3 # 43 about finding the circumcenter of a triangle.

Mon Dec 4 (Meeting Number 39)

Presentation Assignments (Remember to streamline your presentations. The individual steps of basic calculations don't need to be written on the board. Instead, write what calculation was done, and give the result. Only show details of calculations if they are particularly tricky or surprising.)

• Coleman (CP10): Explain what the Circumscribed circle for a triangle is. Then solve 8.3 # 44 about finding the circumscribed circle for a triangle.
• Graham (CP09): Solve 8.3 # 45, but using the second equation y = x/2 - 1 instead of y = x/2 + 1
• Murawski (CP09): Solve 9.1 # 12b (about the translation that takes P to Q)

Wed Dec 6 (Meeting Number 40)

Presentation Assignments (Remember to streamline your presentations. The individual steps of basic calculations don't need to be written on the board. Instead, write what calculation was done, and give the result. Only show details of calculations if they are particularly tricky or surprising.)

• Silveira (CP09): 9.1 # 4 (about translation)
• Murawski (CP10): 9.1 # 6, and (re-try 9.1 # 12 if you want) (both are about translation)
• Bown (CP10): 9.1 # 14 (basic problems about rotation)
• Graham (CP10): 9.1 # 25,26 (basic problems about rotation)
• Rush (CP09): Solve 9.1 # 36 (basic problem about reflection)
• Schweiterman (CP09): Solve 9.1 # 40 (basic problem about glide reflection)

Fri Dec 8 (Meeting Number 41)

Instructions for all three Presentation Assignments

1. Draw triangle A,B,C with vertices A,B,C labeled with their coordinates.
2. Draw lines L and M, labeled with their line equations.
3. Reflect points A,B,C over line L to get new points A',B',C'. (Draw these new points, labeled with their coordinates.)
4. Reflect points A',B',C' over line M to get points A",B",C". (Draw these new points, labeled with their coordinates.)
5. Will any points of the plane after these two reflections have been performed? Explain.
6. The result of the two reflections an isometry. What type? (Must be either a translation, a rotation, a reflection, or a glide reflection.)

The Presentation Assignments

• Rush (CP10): (Similar to suggested problem 9.3 # 7) Let A = (4,3), B = (7,6), and C = (8,4). Let L be the line x = 10 and let M be the line x = 20.
• Schweiterman (CP10): (Similar to suggested problem 9.3 # 8) Let A = (4,3), B = (7,6), and C = (8,4). Let L be the line y = x and let M be the line x = 0.
• Silveira (CP10): (Also similar to suggested problem 9.3 # 8) Same thing as Schweiterman, but use points D,E,F instead of A,B,C. Let D = (7,8), E = (8,12), and F = (10,11). Again let L be the line y = x and let M be the line x = 0.