Name: _______________________________________ Date: _____________ Period: _____
Geometry Chapter 2 Test A
Multiple Choice ~ Each Multiple Choice question is worth 2 points.
1. Write this statement as a conditional in if-then form:
All triangles have three sides.
a. If a triangle has three sides, then all triangles have three sides.
b. If a figure has three sides, then it is not a triangle.
c. If a figure is a triangle, then all triangles have three sides.
d. If a figure is a triangle, then it has three sides.
1.______
2. Which conditional has the same truth value as its converse?
a. If x = 7, then
.
b. If a figure is a square, then it has four sides.
c. If x – 17 = 4, then x = 21.
d. If an angle has measure 80, then it is acute.
2.______
3. 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 an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
a. One statement is false. If an angle measure is 90, the angle may be a vertical angle.
b. One statement is false. If an angle is a right angle, its measure may be 180.
c. Both statements are true. An angle is a right angle if and only if its measure is 90.
d. Both statements are true. The measure of angle is 90 if and only if it is not a right angle.
3.______
4. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a
true biconditional.
Two lines that intersect at right angles are perpendicular.
a. The statement is not reversible.
b. Reversible; if two lines intersect at right angles, then they are perpendicular.
c. Reversible; if two lines are perpendicular, then they intersect at right angles.
d. Reversible; two lines intersect at right angles if and only if they are perpendicular.
4.______
5. Use the Law of Detachment to draw a conclusion from the two given statements.
5.______
If two angles are congruent, then they have equal measures.
and
a.
b.
are congruent.
+
= 90
=
c.
d.
is the complement of
6. Name the Property of Equality that justifies the statement:
If p = q, then
.
a. Reflexive Property
c. Symmetric Property
b. Multiplication Property
d. Subtraction Property
.
6.______
Name: _______________________________________ Date: _____________ Period: _____
7. Find the value of x.
7._____
(7x – 8)°
(6x + 11)°
Drawing not to scale
a. –19
b. 125
c. 19
d. 55
8._____
8. Are points B, J, and C collinear or noncollinear?
a. collinear
b. noncollinear
c. impossible to tell
9._____
9. Name the line and plane shown in the diagram.
T
U
S
R
a.
and plane RSU
b. line R and plane RSU
10. If
scale.
a. 64
and
c.
d.
and plane UR
and plane UT
, then what is the measure of
b. 12
c. 52
11. The supplement of an angle is 25°. What is the measure of the angle?
a. 165°
b. 75°
c. 65°
The diagram is not to
10.____
d. 76
11.____
d. 155°
Name: _______________________________________ Date: _____________ Period: _____
12. Use the Law of Syllogism to draw a conclusion from the two given statements.
If two lines intersect and form right angles, the lines are perpendicular.
If two lines are perpendicular, they intersect and form 90° angles.
a. If two lines do not intersect and form 90° angles, they do not form right angles.
b. The lines are perpendicular.
c. The lines intersect and form 90° angles.
d. If two lines intersect and form right angles, they intersect and form 90° angles.
12.____
Short Answer
13. Write the converse of the statement. If the converse is true, write true; if not true, provide a
counterexample. (4 points)
If x = 4, then x2 = 16.
Fill in each missing reason.
14. Given:
,
Find x. (1 point per blank)
P
, and
R
.
Q
Statements
,
S
Drawing not to scale
Justifications
, and
a.
b.
x – 5 + x – 11 = 100
c.
2x – 16 = 100
d.
2x = 116
x = 58
e.
f.
15. A plumber knows that if you shut off the water at the main valve, it is safe to remove the sink faucet.
The plumber turns the main valve to the “Off” position. What conclusion can the plumber make?
(2 points)
Name: _______________________________________ Date: _____________ Period: _____
16. Complete the proof. (1 point each blank)
Given:
are supplementary, and
are supplementary.
Prove:
Statements
are supplementary
are supplementary
_________________a.
_________________b.
Justifications
Given
Definition of supplementary angles
c.____________________________
_______________d.
________________e.
Subtraction Property of Equality
Definition of congruence
17. Solve for x. Justify each step. (6 points)
Statements
a. 4x – 9 = 99
c.
e.
Justifications
b.
d.
f.
18. 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. (2 points)
If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
19. Write the two conditional statements that make up the following biconditional. (2 points)
I drink juice if and only if it is breakfast time.
Name: _______________________________________ Date: _____________ Period: _____
20. Name the Property of Congruence that justifies the statement: (2 points)
A  A .
21. If T is the midpoint of
S
find the values of x and ST. The diagram is not to scale. (4 points)
T
9x
U
4x + 25
22. Identify the hypothesis and conclusion of this conditional statement: (2 points)
If two lines intersect at right angles, then the two lines are perpendicular.
Vocabulary
Match each word with the definition. (2 points each)
23. ____ Conditional
A. “then” part of the sentence
24. ____ Hypothesis
B. true or false answer to a conditional
statement
25. ____ Conclusion
C. A statement that you can prove true.
26. ____ Truth Value
D. If a = b and b = c, then a = c
27. ____ Converse
E. If a = b, then b = a
28. ____ Symmetric Property
F. if-then statement
29. ____ Theorem
G. a conditional statement with the
hypothesis and conclusion switched.
30. ____ Transitive Property
H. “if” part of the sentence
(BONUS QUESTION ON THE BACK!!!!)
Name: _______________________________________ Date: _____________ Period: _____
Bonus Question (3 points)
23. Given:
Prove:
are complementary, and
are complementary.
Name: _______________________________________ Date: _____________ Period: _____