Geometry A
Unit 2 Test Practice
Name
Date
60
Block
Directions: This quiz is written to assess Unit 2 concepts. Please answer each question to the
best of your ability. If the appropriate work is not shown, then points may be deducted.
1. Which of the following statements restates the sentence below as a conditional? (Circle one).
“A kangaroo has a pouch”
a. All kangaroos have pouches.
b. Some kangaroos have pouches.
c. If it has a pouch, then it’s a kangaroo.
d. If it is a kangaroo, then it has a pouch.
2. Write the hypothesis and conclusion of the conditional below. Also, write the converse,
inverse, and contrapositive. Then, determine each statement’s truth value.
“If we have a snow day, then school is closed.”
T/F:
T
Hypothesis:
Conclusion:
Converse:
T/F:
Inverse:
T/F:
Contrapositive:
T/F:
3. Determine whether the statements are true or false. If false, provide a counterexample.
a. If the month is February, then there are 28 days in the month.
c. If x 2  36 , then x  6 .
d. If 2+2=5, then it rains cats and dogs.
4. Given below are two biconditional statements.
a. Two angles are complementary if and only if they are acute.
b. An angle is obtuse if and only if it has a measure between 90 and 180 degrees.
Which of the two biconditionals is false? Explain why it is false.
Why is the other biconditional true?
5. Which of the following best states the following definition as a biconditional statement?
(Circle one)
Skew lines are non-coplanar lines that do not intersect.
a.
b.
c.
d.
If lines are skew, then they are con-coplanar lines that do not intersect
Lines are skew if and only if they are non-coplanar lines that do not intersect
If lines are non-coplanar and do not intersect, then they are skew lines
Skew lines are lines if and only if they are non-coplanar and do not intersect
6. Determine whether the conclusion is based on inductive or deductive reasoning.
“Cecile talks to her uncle about the presidential elections of 1976, 1980, and 1984. Cecile
concludes that presidential elections happen every four years.”
inductive or
deductive
7. Determine if the conclusion is valid using the Law of Detachment.
If you mow the neighbor’s yard, then you will earn $20.
Jared has $20.
Conclusion: Jared mowed the neighbor’s yard.
Given:
Valid
Invalid
8. Complete the conclusion based on the Law of Syllogism.
If you mow the neighbor’s yard, then you earn $20.
If you earn $20, then you will go to the movies.
Conclusion: If you mow the neighbor’s yard, then
Given:
For questions 9–13, choose the letter that best answers the question.
9. Which of the following is a pair of corresponding angles?
a. 1 and 6
b. 3 and 7
c. 5 and  4
d. 1 and 8
10. Which of the following is a pair of alternate interior angles?
a. 3 and 6
b. 3 and 7
c. 3 and  4
d. 3 and 5
11. Which of the following is a linear pair of angles?
a. 3 and 7
b. 3 and 6
c. 3 and 5
d. 3 and  4
12. Which of the following is a pair of alternate exterior angles?
a. 1 and 7
b. 2 and 7
c. 3 and 7
d.  4 and 7
13. Which is a pair of same-side interior angles?
a. 3 and 2
b. 3 and  4
c. 3 and 5
d. 3 and 6
.
For questions 14 –27, match each statement with the property, definition, postulate, or
theorem that justifies each statement. You may use some choices more than once or not at
all.
14. QRS  QRS
15. If 3 is a right angle, then m3  90
16. AB  CD and CD  EF , so AB  EF
17. If mDEF  mJKL  180 , then DEF and JKL are supplementary angles
18. If 1 and 2 are vertical angles, then 1  2
19. If D is the midpoint of AO , then AD  DO
20. If W is between A and E , then AW  WE  AE
21. If mH  mQ , then H  Q
22. MT  MT
23. If K and L are complementary, then mK  mL  90
24. If f  g , then f  7  g  7
25. If 1 and 2 are right angles, then 1  2
26. If EF bisects DEG , then DEF  FEG
27. If G in interior of NKL , then mNKG  mGKL  mNKL
28. Find mKLM . You must show work and state the theorem / postulate you used to justify your
steps.
Thm/Post: _______________________________________
mKLM ________
29. Find mDEF . You must show work and state the theorem / postulate you used to justify your
steps.
Thm/Post: _______________________________________
mDEF ________
For questions 30–36, determine whether the given information is enough to prove a b .
If so, state the theorem/postulate that justifies your conclusion
If it is not, determine whether there is “not enough info” or the lines are “not parallel”
30. m3  150 , m6  30
31. 4  8
32. 1  3
33. m4  50 , m6  50
34. m2  80 , m8  80
35. m6  40 , m3  120
36. m5  115 , m6  65
37. Write the proof of the Right Angle Congruence Theorem. [hint – this is in your notes, and may
appear on the test; or it could be the Linear Pair Theorem or the Vertical Angles Theorem]
Given:
Prove:
Statement
Reason
1.
2.
3.
4.
38. Complete the proof of the Congruent Complements Theorem.
Given:
1 and 2 are complementary
2 and 3 are complementary
Prove:
1  3
Statement
1.
2.
3.
4.
5.
6.
7.
8.
9.
Reason
Given
Definition of complementary angles
Given
Transitive Property of Equality
m2  m2
m1  m2  m2  m2  m2  m3
Simplify
39. Complete the proof.
Given: 1  4
Prove: 2  3
Statement
1. 1  4
2. 1  2
3. 3  4
4. 2  4
5. 2  3
Reason
40. The reasons needed to complete the proof are given below the proof. Put them in the proper
places to complete.
Given: AXB  CXD
Prove: AXC  BXD
Statement
1.
2.
3.
4.
5.
6.
7.
Reason
AXB  CXD
mAXB  mCXD
mAXB  mBXC  mBXC  mCXD
mAXB  mBXC  mAXC
mBXC  mCXD  mBXD
mAXC  mBXD
AXC  BXD
Add Prop =
Def ≅ ∠’s
Def ≅ ∠’s
∠ Add Post
Substitution
∠ Add Post
Given