Name:______________________________Date:___________________Period:__________
Geometry Chapter 2 Test B
Short Answer
Fill in each missing reason. (1 point per blank)
P
1. Given:
Find x.
,
, and
R
.
Q
S
Drawing not to scale
Statements
,
Justifications
, and
a.
b.
c.
x – 3 + x + 11 = 100
d.
2x + 8 = 100
e.
2x = 92
f.
x = 46
2. Write the two conditional statements that make up the following biconditional. (2 points)
I drink juice if and only if it is breakfast time.
3. Write the converse of the statement. If the converse is true, write true; if not true, provide a
counterexample. (4 points)
If x = 12, then x2 = 144.
4. 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
6x + 18
Name:______________________________Date:___________________Period:__________
5. 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.
6. Complete the paragraph proof. (1 point per 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
7. 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:__________
8. Solve for x. Justify each step. (6 points)
Statements
Justifications
b.
a. 2x – 14 = 82
d.
c.
f.
e.
9. Name the Property of Congruence that justifies the statement: (2 points)
 B  B .
10. 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)
11. ____ Conditional
A. If a = b and b = c, then a = c
12. ____ Hypothesis
B. true or false answer to a conditional
statement
13. ____ Conclusion
C. A statement that you can prove true.
14. ____ Truth Value
D. “then” part of the sentence
15. ____ Converse
E. If a = b, then b = a
16. ____ Symmetric Property
F. a conditional statement with the
hypothesis and conclusion switched.
17. ____ Theorem
G. “if” part of the sentence
18. ____ Transitive Property
H. if-then statement
Name:______________________________Date:___________________Period:__________
Multiple Choice ~Each multiple choice question is worth 2 points
19. Use the Law of Detachment to draw a conclusion from the two given statements.
19.______
If two angles are congruent, then they have equal measures.
and
a.
b.
are congruent.
c.
d.
=
+
= 90
is the complement of
20. 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 is a triangle, then all triangles have three sides.
c. If a figure has three sides, then it is not a triangle.
d. If a figure is a triangle, then it has three sides.
21. Name the line and plane shown in the diagram.
.
20.______
21.______
T
U
S
R
a.
b.
c. line R and plane RSU
and plane UR
d.
and plane UT
and plane RSU
22. Find the value of x.
22.______
(8x – 6)°
(7x + 8)°
Drawing not to scale
a. 106
b. 74
c. 14
d. –14
23. Name the Property of Equality that justifies the statement:
If x = y, then
.
a. Division Property
c. Symmetric Property
b. Subtraction Property
d. Transitive Property
23.______
24. The supplement of an angle is 48°. What is the measure of the angle?
a. 52°
b. 132°
c. 142°
24.______
d. 42°
Name:______________________________Date:___________________Period:__________
25.
Are points C, J, and B collinear or noncollinear?
a. collinear
b. noncollinear
25._____
c. impossible to tell
26. 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. Both statements are true. An angle is a right angle if and only if its measure is 90.
b. One statement is false. If an angle is a right angle, its measure may be 180.
c. One statement is false. If an angle measure is 90, the angle may be a vertical angle.
d. Both statements are true. The measure of angle is 90 if and only if it is not a right angle.
27._____
27. Which conditional has the same truth value as its converse?
a. If a figure is a square, then it has four sides.
b. If x = 7, then
.
c. If x – 17 = 4, then x = 21.
d. If an angle has measure 80, then it is acute.
28. If
scale.
a. 54
and
, then what is the measure of
b. 56
c. 2
26._____
The diagram is not to
28._____
d. 52
29. Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a 29._____
true biconditional.
Two lines that intersect at right angles are perpendicular.
a. Reversible; two lines intersect at right angles if and only if they are perpendicular.
b. The statement is not reversible.
c. Reversible; if two lines are perpendicular, then they intersect at right angles.
d. Reversible; if two lines intersect at right angles, then they are perpendicular.
Name:______________________________Date:___________________Period:__________
30. 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 900 angles.
a. If two lines do not intersect and form 900 angles, they do not form right angles.
b. The lines intersect and form 900 angles.
c. The lines are perpendicular.
d. If two lines intersect and form right angles, they intersect and form 900 angles.
Bonus Question (3 points)
23. Given:
Prove:
are complementary, and
are complementary.
30.______
Name:______________________________Date:___________________Period:__________