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Transcript
Geometry Unit 2 Review
Name: ______________________________
Use the following diagram for problems 1 -3.
E
2
3
A
6
9
8
D
7
1
11
5
10
12
4
13
1.
B
C
Given the diagram above identify a pair of angle for each of the following types.
o Vertical Angles ________________
o Complementary Angles ___________
o Linear Pair _______________
o Adjacent Angles___________
2. The m11  (3x) and the m12  (2 x  5) . Find the measure of each angle.
Geometry Unit 2 Review
3. Given:
m // n // p
Name: ______________________________
Determine whether each statement is true or false. If the statement is false, change it
to make it true.
a.  A and C are complementary because they form a linear
pair.
b.
t
 B and C are congruent because they are alternate interior
A
m
d.
H and  L are congruent because they are corresponding
angles formed by parallel lines.
G
E
n
H
F
F and C are equal in measure because they are alternate
interior angles formed by parallel lines.
e.
D
B
angles formed by parallel lines.
c.
C
I
p
K
J
I and  B are supplementary because they are same-side
L
interior angles formed by parallel lines.
t
4. Given:
m // n // p .

If m C = 120 , determine the measures of
A
m
C
D
B
all the angles.
G
E
n
H
F
I
p
K
J
L
B
5. Given that AB  AD and AB  BC .
Which of the following conclusions do you know is true?
(Choose one)
A
 A. AB  DC
C
 B. AD  DC
 C.
 D.
AB // DC
AD// BC
D
6. For the given information, tell which pair of lines, if any, must be parallel. Name the postulate or
theorem that supports your answer.
l
o
m
n
Given: m  13 = m  15. Which two lines (if any) are parallel?
1
o
Given: m  4= m  20. Which two lines (if any) are parallel?
o
Given: m  3 = m  13. Which two lines (if any) are parallel?
2
7
3
8
9
13
18
14
19
p5
4
10
6
11 12
15
20
16
21
q
17 1
22
Geometry Unit 2 Review
Name: ______________________________
Write an equation for a line that is parallel to the given line and passes through the given point:
−1
7. Parallel to 𝑦 = 𝑥 − 3 and through (6, 2)
3
8. Parallel to 𝑦 − 7 = 2(𝑥 + 8) and though (1, -2)
Write an equation for a line perpendicular to the given line and passes through the given point:
1
10. Perpendicular to 𝑦 = 2 𝑥 − 1 and through
(-4, 1).
11. Perpendicular to 𝑦 − 2 = −3(𝑥 + 7) and through (3, 0).
Geometry Unit 2 Review
Name: ______________________________
12. Which is the counterexample that proves the conjecture false?
“If two rays have the same endpoint, then they are opposite rays.”
F
H
G
J
13. Identify the hypothesis of the conditional statement “Two angles are complementary if the sum of their
measures is 90 degrees.”
A if
BTwo angles are complementary
C the sum of their measures is
90 degrees
D Two angles are complementary if the sum of their measures is 90 degrees.
14. What is the inverse of the statement
“If two coplanar lines do not intersect, then they are parallel”?
A If two coplanar lines do not intersect, then they are not parallel.
B If two coplanar lines intersect, then they are not parallel.
C If two lines are parallel, then they are coplanar and do not intersect.
D If two coplanar lines are not parallel, then they intersect.
15. Which conjecture is valid by the Law of Syllogism for the following scenario?
“If Joe buys Nancy a card, he will give it to her. If Nancy is having a birthday, then Joe will buy her a card.”
F If Nancy is having a birthday, then Joe will give her a card.
G If Joe buys Nancy a card, then she
is having a birthday.
H If Joe gives Nancy a card, then he bought the card.
J If Joe gives Nancy a card, then she
is having a birthday.
16. Consider the related bi-conditional statement for the conditional statement “If Shelly lives in Texas, then
she lives in the United States.”
Which of the following statements is true about the related bi-conditional statement?
A The bi-conditional is true because the conditional is true.
B The bi-conditional is false because the conditional and its converse are false.
C The bi-conditional is true because the conditional and its converse are true.
D The bi-conditional is false because the converse of the conditional is false.