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.

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

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

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

**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.

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

**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.

**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.

**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

**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.

**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.

**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.

**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.

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

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

**Coleman (CP05):**Solve 5.2 # 26

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

**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

**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.

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

**Bown (CP06):**6.1 # 40, 44

**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:- (This is 6.2 # 19) Prove that if trapezoid
*ABCD*is isosceles, then triangle*AED*~ triangle*CEB*. - If trapezoid
*ABCD*is isosceles, what is the relationship between triangle*AEB*and triangle*CED*? - If trapezoid
*ABCD*is*not*isosceles, what is the relationship between triangle*AED*and triangle*CEB*? - If trapezoid
*ABCD*is*not*isosceles, what is the relationship between triangle*AEB*and triangle*CED*?

- (This is 6.2 # 19) Prove that if trapezoid
**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

**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.)

**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

**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

**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

**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

**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**

**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.

**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*)

**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)

**Instructions for all three Presentation Assignments**

- Draw triangle
*A,B,C*with vertices*A,B,C*labeled with their coordinates. - Draw lines
*L*and*M*, labeled with their line equations. - Reflect points
*A,B,C*over line*L*to get new points*A',B',C'*. (Draw these new points, labeled with their coordinates.) - Reflect points
*A',B',C'*over line*M*to get points*A",B",C"*. (Draw these new points, labeled with their coordinates.) - Will any points of the plane after these two reflections have been performed? Explain.
- 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.

(page maintained by Mark Barsamian, last updated Dec 4, 2017 )