Geometry Chapter 2 Practice Test
1. Write this statement as a conditional in if-then form, then write it’s converse.
All supplementary angles have a sum of 180 degrees.
2. Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional.
If either is false, give a counterexample.
If two angles are vertical angles, then they are congruent.
If two angles are congruent, then they are vertical angles.
3. Use the Law of Detachment to draw a conclusion from the two given statements.
If two angles are complimentary, then the sum of their measures is 90.
and
are complimentary.
4. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements.
If the bus arrives after 7:31, then we will be late for school.
If we are late for school, we will get detention.
Our bus arrived at 7:42.
5. Name the Property of Equality that justifies the statement:
If XY + JM = GT + XY, then JM = GT
6. Find the value of x.
(6x + 2)°
(7x – 13)°
Drawing not to scale
7. Are points B, F, and E collinear or noncollinear?
8. Name the line and plane shown in the diagram.
R
S
P
9. If
and
Q
, then what is the measure of
The diagram is not to scale.
10. The complement of an angle is 61°. What is the measure of the angle?
Short Answer
11. Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 9, then x2 = 81.
Fill in each missing reason.
12. Given:
4x
2x + 1
Drawing not to scale
13. Given:
Find x.
,
P
, and
.
R
Q
S
Drawing not to scale
x + 9 + x + 5 = 100
2x + 14 = 100
2x = 86
x = 43
a. __________________
b. __________________
c. __________________
d. __________________
e. __________________
14. Name the Property of Congruence that justifies the statement:
If DE  GH and GH  KL , then DE  KL
15. Find BD. (Show all work!!!)
A
B
C
D
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10
16. If T is the midpoint of
S
find the values of x and ST. The diagram is not to scale.
T
3x
U
2x + 21
17. Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
18. Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a
good definition. Explain.
A figure is a polygon if and only if it has three or more sides.
Essay
19. Given:
Prove:
are complementary, and
are complementary.
Geometry Chapter 2 Test
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
D
C
C
B
A
D
A
A
A
A
D
SHORT ANSWER
12. If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to –4.
13. a. Segment Addition Postulate
b. Substitution
c. Simplify
d. Subtraction Property of Equality
e. Division Property of Equality
14. Angle Addition Postulate; Addition Property of Equality
15. a. 180
b. 180
c. Transitive Property (or Substitution Property)
d.
e.
16. It is safe to remove the sink faucet.
17. Symmetric Property
18. 12
19. x = 5, ST = 45
20. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.
ESSAY
21.
[4]
[3]
By the definition of complementary angles,
and
the Transitive Property of Equality (or Substitution Property),
. By the Subtraction Property of Equality,
by the definition of congruent angles.
OR
equivalent explanation
one step missing OR one incorrect justification
. By
, and
[2]
[1]
two steps missing OR two incorrect justifications
correct steps with no explanations
OTHER
22. A figure is a polygon if it has three or more sides.
If a figure is a polygon, then it has three or more sides.
The biconditional is not a good definition.
A figure with three or more sides may not be a closed figure.