Geometry Homework Worksheets: Chapter 2

HW Set #1: Problems #1 - 8
For #1-4, choose the best answer for each multiple choice question.
1. Which of the following statements is/are always true? / 2. Identify the converse of the conditional statement below:
I. adjacent angles are acute
II. if , then is acute
III. two acute angles make a right angle
A. I only
B. II only
C. III only
D. both I and II
E. I, II, and III / If I break my iPod, I will get in trouble.
A. If I don’t break my iPod, I won’t get in trouble.
B. If I break my iPod, I will get in trouble.
C. If I get in trouble, I will break my iPod.
D. If I don’t get in trouble, I didn’t break my iPod.
E. none of the above
3. Identify a counterexample to the given statement:
If is obtuse, then
A. is an acute angle
B. is a right angle
C.
D.
E. / 4. All of the following statements are true except:
A. Opposite rays share an endpoint.
B. The intersection of two planes is a point.
C. Four non-coplanar points determine space.
D. Obtuse angles measure more than 90 degrees.
E. Congruent segments have the same length.
For questions 5-8 translate each of the following into a mathematical expression.
5. The difference of four times a number and seven. / 6. Three times the difference of a number and two.
7. The sum of two and the quotient of a number and five. / 8. The product of four times a number and nine.

HW Set #2 (Problems 9-15)

For #9-12, choose the best answer for each multiple choice question.
9. If and are supplementary angles, what angle relationship between CANNOT be true?
(A) are right angles
(B) are adjacent angles
(C) are complementary angles
(D) are congruent angles / 10. Which number is a counterexample to the statement below?
All prime numbers are odd.
(A) 0 (B) 2 (C) 34 (D) 86
11. What value of x is a counterexample to the statement below?
If , then .
(A) 4 (B) 2 (C) -2 (D) -3 / 12. Which statement is NOT true?
(A) If two lines are parallel, then they lie in one plane and do not intersect.
(B) Two lines lie in one plane if and only if the lines are parallel.
(C) If two coplanar lines do not intersect, then the lines are parallel.
(D) Two lines lie in one plane and do not intersect if and only if the two lines are parallel.
For questions 13-14, solve each equation. If necessary, leave your answers as reduced fractions.
13. / 14.
For questions 15-16 translate each of the following into a mathematical expression.
15. Seven less than twice a number / 16. Eight more than the quotient of seven and x.
HW Set #3: Problems #16-22
For #16-22, choose the best answer for each multiple choice question.
16. The following statement is an example of which property:
If , then .
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Multiplication Property of Equality
D. Division Property of Equality
E. Distributive Property of Equality / 17. The following statement is an example of which property?
-11xy+ 2x2 = – 11xy + 2x2
A. Transitive Property of Equality
B. Symmetric Property of Equality
C. Reflexive Property of Equality
D. Substitution Property of Equality
E. Distributive Property of Equality
Choose the best answer for each multiple choice question. For #18-22, you are completing a proof.
Given: 5(2x – 6) = 4x + 6
Prove: x = 6
Statements: / Reasons
1.) 5(2x – 6) = 4x + 6
2.) 10x – 30 = 4x + 6
3.) ______#20______
4.) 6x = 36
5.) x = 6 / 1.) ______#18______
2.) ______#19______
3.) Subtraction Property of Equality
4.) ______#21______
5.) ______#22______
18. What reason should be written in the space marked #18 of this proof?
A. Given
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property / 19. What reason should be written in the space marked #19 of this proof?
A. Substitution Property of Equality
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property
20.What statement should be written in the space marked #20 of this proof?
A. 10x = 4x + 36
B. 6x = 36
C. 6x – 30 = 6
D. None of these / 21. What reason should be written in the space marked #21 of this proof?
A. Substitution Property of Equality
B. Subtraction Property of Equality
C. Distributive Property of Equality
D. Addition Property of Equality
E. Reflexive Property
22. What reason should be written in the space marked #22 of this proof?
A. Subtraction Property of Equality
B. Division Property of Equality
C. Prove
D. Addition Property of Equality
E. Multiplication Property of Equality
HW Set #4: Problems #23-28
For #23-26, choose the best answer for each multiple choice question.
Choose the best answer for each multiple choice question. For #23-26, you are completing a proof.
Given: AB = XY, BC = YZ
Prove: AC = XZ
Statements / Reasons
1.) AB = XY
BC = YZ
2.) AB + BC = XY + YZ
3.) AC = AB + BC
XZ = XY + YZ
4.) _____#25______/ 1.) Given
2.) _____#23______
3.) _____#24______
4.) _____#26______
23. What reason should be written in the space marked #23 of this proof?
A. Substitution Property of Equality
B. Subtraction Property of Equality
C. Segment Addition Postulate
D. Addition Property of Equality
E. Definition of Midpoint / 24. What reason should be written in the space marked #24 of this proof?
A. Addition Property of Equality
B. Subtraction Property of Equality
C. Segment Addition Postulate
D. Definition of Midpoint
E. Transitive Property of Equality
25. What statement should be written in the space marked #25 of this proof?
A. AB = XY, BC = YZ
B. AC = XZ
C. AC + XZ = AB + XY + BC + YZ
D. B is the midpoint of
E. Y is the midpoint of / 26. What reason should be written in the space marked #26 of this proof?
A. Prove
B. Addition Property of Equality
C. Subtraction Property of Equality
D. Substitution Property of Equality
E. Segment Addition Postulate
For questions 27-28, fill in the reasons for each of the given statements.
27. Given: RT = SU and the figure at the
right.
Prove: RS = TU
Statements: /
Reasons:
1.) RT = SU
2.) ST = ST
3.) RT – ST = SU – ST
4.) RT – ST = RS
5.) SU – ST = TU
6.) RS = TU / 1.)
2.)
3.)
4.)
5.)
6.)
28. Given: M is the midpoint of
Prove:
Statements: /

Reasons:
1.) M is the midpoint of
2.)
3.) AM = MB
4.) AM + MB = AB
5.) AM + AM = AB
6.) / 1.)
2.)
3.)
4.)
5.)
6.)
HW#5: Problems #29-34
For questions 29-32, complete the two column proof for each situation.
29. Given: M is the midpoint of
N is the midpoint of
AB = CD
Prove: AM = CN
Statements:
1.)
2.)
3.)
4.)
5.) AM + AM = CN + CN
6.) 2AM = 2CN
7.) / Reasons:
1.)
2.) Def. of midpoint
3.) SAP
4.) Substitution prop. of equality
5.)
6.)
7).
30. Given: is an angle bisector of
Prove:
Statements:
1.)
2.)
3.)
4.)
5.)
6.) / Reasons:
1.)
2.)
3.)
4.)
5.)
6.)
31. Given: RT = 5, RS = 5,
Prove:
Statements:
1.)
2.) RT = RS
3.)
4.)
MORE ON THE NEXT PAGE!! / Reasons:
1.)
2.)
3.) Def. of congruent segments
4.)
32. Given: are complements
are complements

Prove:
Statements:
1.)
2.)
3.)
4.)
5.)
6.) / Reasons:
1.)
2.) Def. of complementary angles
3.)
4.)
5.) Subtraction prop. of equality
6.)
For questions 33-34, set up an equation & solve to find the unknown angle measurement.
33. The sum of an angle, its complement, and its supplement is 200˚. Find the angle / 34. The sum of an angle, its complement, and four times its supplement is 690˚.
HW#6: Problems #35-49
For questions 35-38, simplify each expression as much as possible. If necessary, leave your answers as reduced fractions.
35. / 36.
37. / 38.
For questions 39-40, find the midpoint of the segment with the given endpoints.
39. (-8, 9) and (-2, -6) / 40. (7, -5) and (-9, -13)
For questions 41-44, solve each equation. If necessary, leave your answers as reduced fractions.
41. / 42.
43. / 44.
45. Find the missing endpoint of if H has coordinates (5, -2) and the midpoint of is (-4, 8).
For questions 46-49, find the value of the variable(s).
46. / 47.
48. / 49.