Name: ________________________ Class: ___________________ Date: __________ ID: A

Geometry Chapter 1-2 Exam

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1. Based on the pattern, what is the next figure in 4. Name an angle supplementary to ∠COB.
the sequence?

a.

b.

c.

d.
a. ∠AOE
b. ∠BOE
c. ∠COD
2. If T is the midpoint of SU, find the values of x d. ∠BOA
and ST. The diagram is not to scale. 5. Supplementary angles are two angles whose
measures have the sum of ____.
Complementary angles are two angles whose
measures have the sum of ____.
a. 180; 90
a. x = 8, ST = 24
b. 90; 180
b. x = 8, ST = 36
c. 90; 45
c. x = 3, ST = 24
d. 180; 360
d. x = 3, ST = 36
6. The complement of an angle is 36°. What is the
3. If m∠EOF = 20 and m∠FOG = 36, then what
measure of the angle?
is the measure of ∠EOG? The diagram is not to
a. 54°
scale.
b. 144°
c. 154°
d. 64°
7. Find the distance between points P(6, 4) and Q(5,
6) to the nearest tenth.
a. 2.2
b. 5
c. 3
d. 14.9
a. 40
b. 16
c. 56
d. 72

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8. Each unit on the map represents 1 mile. What is Find the length of the missing side. The
the actual distance from Oceanfront to Seaside? triangle is not drawn to scale.
Round your answer to the nearest whole number.
11.

a. 10
b. 9
c. 100
d. 12
a. about 9 miles
b. about 7 miles Find the length of the missing side. Leave
c. about 8 miles your answer in simplest radical form.
d. about 10 miles
9. Find the coordinates of the midpoint of the 12.
segment whose endpoints are H(9, 4) and K(7, 2).
a. (16, 6)
b. (1, 1)
c. (2, 2)
d. (8, 3)
10. M(7, 4) is the midpoint of RS. The coordinates
of S are (9, 6). What are the coordinates of R?
a. (5, 2)
b. (11, 8) a. 6 cm
c. (8, 5)
b. 218 cm
d. (14, 8)
c. 2 5 cm
d. 2 30 cm
13. A triangle has sides of lengths 8, 15, and 17. Is it
a right triangle? Explain.
2 2 2
a. no; 8 + 19 ≠ 14
2 2 2
b. no; 8 + 15 ≠ 17
2 2 2
c. no; 8 + 19 = 14
2 2 2
d. yes; 8 + 15 = 17

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14. Find a counterexample to show that the 18. ∠BDA is a straight angle. Find m∠BDC.
conjecture is false.
Conjecture: Any number that is divisible by 5 is
also divisible by 10.
a. 32
b. 50
c. 40
d. 25
15. Identify the segment bisector of AB. Then find
BM.

a. 16°
b. 112°
c. 60°
d. 68°
19. The measure of an angle is nine times the
measure of its complement. Find the measure of
the larger angle.
a. 80°
a. line M; BM = 12 b. 162°
b. M; BM = 49 c. 160°
c. M; BM = 12 d. 81°
d. line M; BM = 49 20. Find the values of x and y.
16. Find the area of FGH with coordinates
F ÊÁË −4, 6 ˆ˜¯ ,G ÊÁË −2, −1 ˆ˜¯ , and H ÊÁË 2, 6 ˆ˜¯ .
a. 7 square units
b. 21 square units
c. about 21.34 square units
d. 42 square units
17. In the diagram, m∠BDA = 144°. Find m∠ADC.

a. x = 20, y = 2
b. x = 8, y = 14
c. x = 20, y = 14
d. x = 8, y = 2

a. 91°
b. 82°
c. 62°
d. 40°

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Name: ________________________ ID: A

21. Let p be “you are a senior” and let q be “you are

in high school.” Write the converse. Then decide
whether it is true or false.
a. If you are a senior, then you are in high
school; true
b. If you are in high school, then you are a
senior; false
c. If you are not a senior, then you are not in
high school; false
d. If you are not in high school, then you are
not a senior; true

Short Answer

22. Complete the proof.

Given AB = CD
Prove AC = BD

STATEMENTS REASONS
1. AB = CD 1. Given
2. BC = BC 2.
3. AB + BC = CD + BC 3. Addition Property of Equality
4. 4. Segment Addition Postulate
5. CD + BC = BD 5. Segment Addition Postulate
6. 6. Substitution Property of Equality

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Fill in each missing reason.

23. Given: m∠AOC = 150

m∠AOB + m∠BOC = m∠AOC a. ____

2x + 6(x − 3) = 150 b. ____

2x + 6x − 18 = 150 c. ____

8x − 18 = 150 d. ____

8x = 168 e. ____

x = 21 f. ____

Free Response

24. Use the given information to make a two column proof.

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Geometry Chapter 1-2 Exam

Answer Section

MULTIPLE CHOICE

1. ANS: C PTS: 1 DIF: L2 REF: 1-1 Patterns and Inductive Reasoning

OBJ: 1-1.1 Using Inductive Reasoning STA: CA GEOM 1.0| CA GEOM 3.0
TOP: 1-1 Example 1 KEY: pattern | inductive reasoning
2. ANS: C PTS: 1 DIF: L2 REF: 1-5 Measuring Segments
OBJ: 1-5.1 Finding Segment Lengths TOP: 1-5 Example 3
KEY: segment | segment length | midpoint | multi-part question
3. ANS: C PTS: 1 DIF: L2 REF: 1-6 Measuring Angles
OBJ: 1-6.1 Finding Angle Measures TOP: 1-6 Example 3
KEY: Angle Addition Postulate
4. ANS: B PTS: 1 DIF: L2 REF: 1-6 Measuring Angles
OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4
KEY: supplementary angles
5. ANS: A PTS: 1 DIF: L2 REF: 1-6 Measuring Angles
OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4
KEY: supplementary angles | complementary angles
6. ANS: A PTS: 1 DIF: L2 REF: 1-6 Measuring Angles
OBJ: 1-6.2 Identifying Angle Pairs TOP: 1-6 Example 4
KEY: complementary angles
7. ANS: A PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane
OBJ: 1-8.1 Finding Distance on the Coordinate Plane TOP: 1-8 Example 1
KEY: Distance Formula | coordinate plane
8. ANS: C PTS: 1 DIF: L3 REF: 1-8 The Coordinate Plane
OBJ: 1-8.1 Finding Distance on the Coordinate Plane
KEY: coordinate plane | Distance Formula | word problem | problem solving
9. ANS: D PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane
OBJ: 1-8.2 Finding the Midpoint of a Segment TOP: 1-8 Example 3
KEY: coordinate plane | Midpoint Formula
10. ANS: A PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane
OBJ: 1-8.2 Finding the Midpoint of a Segment TOP: 1-8 Example 4
KEY: coordinate plane | Midpoint Formula
11. ANS: A PTS: 1 DIF: L1
REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem
NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3
TOP: 8-1 Example 1 KEY: Pythagorean Theorem | leg | hypotenuse
MSC: NAEP G3d | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP |
S9.TSK2.GM | S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.52
12. ANS: D PTS: 1 DIF: L2
REF: 8-1 The Pythagorean Theorem and Its Converse OBJ: 8-1.1 The Pythagorean Theorem
STA: CA GEOM 15.0 TOP: 8-1 Example 2
KEY: Pythagorean Theorem | leg | hypotenuse

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13. ANS: D PTS: 1 DIF: L1

REF: 8-1 The Pythagorean Theorem and Its Converse
OBJ: 8-1.2 The Converse of the Pythagorean Theorem
NAT: NAEP 2005 G3d | ADP I.4.1 | ADP J.1.6 | ADP K.1.2 | ADP K.5 | ADP K.10.3
TOP: 8-1 Example 4 KEY: Pythagorean Theorem
MSC: NAEP G3d | CAT5.LV20.50 | CAT5.LV20.55 | CAT5.LV20.56 | IT.LV16.AM | IT.LV16.CP |
S9.TSK2.GM | S9.TSK2.PRA | S10.TSK2.GM | S10.TSK2.PRA | TV.LV20.13 | TV.LV20.14 | TV.LV20.52
14. ANS: D PTS: 1 DIF: L2 REF: 1-1 Patterns and Inductive Reasoning
OBJ: 1-1.1 Using Inductive Reasoning STA: CA GEOM 1.0| CA GEOM 3.0
TOP: 1-1 Example 3 KEY: conjecture | counterexample
15. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.3
NAT: HSG-GPE.B.7 KEY: segment bisector
NOT: Example 2
16. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.4
NAT: HSG-GPE.B.7 | HSG-MG.A.1 KEY: coordinate plane | area
NOT: Example 3
17. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.5
NAT: HSG-CO.A.1 KEY: measure of an angle | angle
NOT: Example 4
18. ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.5
NAT: HSG-CO.A.1 KEY: measure of an angle | angle
NOT: Example 4
19. ANS: D PTS: 1 DIF: Level 2 REF: Geometry Sec. 1.6
NAT: HSG-CO.A.1 KEY: complementary angles
NOT: Example 5
20. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 2.6
NAT: HSG-CO.C.9 KEY: using angle relationships
NOT: Example 4-2
21. ANS: B PTS: 1 DIF: Level 2 REF: Geometry Sec. 2.1
NAT: HSG-CO.C.9 | HSG-CO.C.10 | HSG-CO.C.11 | HSG-SRT.B.4
KEY: conditional statement | converse | inverse | contrapositive | application
NOT: Example 3

SHORT ANSWER

22. ANS:
Statement 4: AB + BC = AC, Statement 6: AC = BD, Reason 2: Reflexive Property of Equality

PTS: 1 DIF: Level 1 REF: Geometry Sec. 2.5

NAT: HSG-CO.C.9 KEY: properties of equality
NOT: Application-1

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23. ANS:
a. Angle Addition Postulate
b. Substitution Property
c. Distributive Property
d. Simplify
e . Addition Property of Equality
f. Division Property of Equality

PTS: 1 DIF: L3 REF: 2-4 Reasoning in Algebra

OBJ: 2-4.1 Connecting Reasoning in Algebra and Geometry STA: CA GEOM 1.0| CA GEOM 3.0
TOP: 2-4 Example 1
KEY: proof | deductive reasoning | Properties of Equality | multi-part question

OTHER

24. ANS:

461 mi; If the round-trip distance between City Y and City X is 126 miles, then the one-way distance is 63
miles. If the round-trip distance between City X to City Z is 796 miles, then the one-way distance is 398
miles. 63 + 398 = 461

PTS: 1 DIF: Level 3 REF: Geometry Sec. 1.2

NAT: HSG-CO.A.1 KEY: distance | application
NOT: Example 4