Chapter 1 ● Assessments 1043

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Pre-Test

Name ________________________________________________________ Date __________________________

1. Sketch and label an example of each statement.

a.

___ › HG b. �A � �B

c. ‹

___ › ST �

‹

___ › UV d. M is the midpoint of

___

PQ .

e. Angles 1 and 2 are vertical angles. f. Angle C is a right angle.

2. Construct an angle that is one fourth the measure of �X.

X

3. What is an angle bisector?

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Pre-Test PAGE 2

4. The measure of angle T is 70°.

a. What is the measure of an angle that is complementary to �T?

b. What is the measure of an angle that is supplementary to �T?

5. Line segment AB has midpoint M. If the measure of line segment AB is equal to 4 inches, what is the

measure of line segment AM?

6. The first four numbers in a sequence are 5, 17, 29, and 41.

a. What is the next number in the sequence? How did you calculate the next number?

b. What types of reasoning did you use and in what order to make the conclusion?

7. Consider the conditional statement: If M is the midpoint of ___

AB , then ____

AM � ____

MB .

a. What is the hypothesis p?

b. What is the conclusion q?

c. What is the truth value of a conditional statement if p and q are true?

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Pre-Test PAGE 3

Name ________________________________________________________ Date __________________________

8. Create a two-column proof.

N POM

Given: MN � OP

Prove: ____

MO � ___

NP

Statements Reasons

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Post-Test

Name ________________________________________________________ Date __________________________

1. Sketch and label an example of each statement.

a. ‹

__ › HI �

‹

___ › JK b. Angle R is acute.

c. �D � �E

d. Angle 4 and �5 are vertical angles. e. W is the midpoint of ___

VX .

f. ___

FG

2. Construct an angle that is one fourth the measure of �1.

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Post-Test PAGE 2

3. What does it mean when a line segment is bisected?

4. The measure of angle S is 50°.

a. What is the measure of an angle that is complementary to �S?

b. What is the measure of an angle that is supplementary to �S?

5. Line segment DE has midpoint M. If the measure of line segment DM is equal to 3 inches, what is the

measure of line segment DE?

6. The first four numbers in a sequence are 5, 15, 45, and 135.

a. What is the next number in the sequence? How did you calculate the next number?

b. What types of reasoning did you use and in what order to make the conclusion?

7. Consider the conditional statement: If

___ › EG bisects �DEF, then m�DEG � m�GEF.

a. What is the hypothesis?

b. What is the conclusion?

c. What is the truth value of a conditional statement if p is true and q is false?

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Post-Test PAGE 3

Name ________________________________________________________ Date __________________________

8. Create a two-column proof.

A

B C

D

E

Given: m�ABE � m�DBC

Prove: �ABD � �EBC

Statements Reasons

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Chapter 1 ● Assessments 1051

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Mid-Chapter Test

Name ________________________________________________________ Date __________________________

1. Sketch and describe all possible relationships between a line and a plane.

2. Construct a line segment with a length equal to AB � CD.

A B

C D

3. Use the diagram shown to determine the measure of each angle. Then classify each angle.

90 10080

11070

12060 130

50 14040

15030

16020

17010

80

10070

11060

12050

130

4014

0

3015

0

2016

0

10 170

F

B

AE

C

D

a. �AFD b. �AFB

c. �EFD d. �EFB

e. �DFB f. �CFA

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Mid-Chapter Test PAGE 2

4. Construct the angle bisector of �A.

A

5. The supplement of an angle is three times the measure of the angle. What is the measure of

each angle? Explain.

6. Construct a line perpendicular to ‹

___ › AB through point C.

A B

C

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Mid-Chapter Test PAGE 3

Name ________________________________________________________ Date __________________________

7. Sketch and label each of the following geometric figures.

a. Adjacent complementary angles �ABC and �CBD

b. Two intersecting lines with vertical angles 1 and 2 and vertical angles 3 and 4

c. Name all of the linear pairs in the figure from part (b).

d. Name the congruent angles and the supplementary angles in the figure from part (b).

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Chapter 1 ● Assessments 1055

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End of Chapter Test

Name ________________________________________________________ Date __________________________

1. State the Segment Addition Postulate.

2. Describe the relationship between supplements of congruent angles.

3. Use the following line segments to construct a line segment that is equal to 2AB � CD.

BA

DC

Match each term with its description.

4. obtuse angle a. two angles whose measures add up to 90°

5. complementary angles b. two nonadjacent angles that are formed by two intersecting lines

6. adjacent angles c. two angles whose measures add up to 180°

7. vertical angles d. an angle whose measure is greater than 90° but less than 180°

8. supplementary angles e. two angles that share a common vertex and a common side

9. Construct the bisector of �K.

K

10. A complement of an angle measures 10 degrees more than the measure of the angle. What is the

measure of the angle and its complement? Explain.

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End of Chapter Test PAGE 2

11. Allergies cause some people to sneeze. Caroline sneezes after she pets her friend’s cat. She also began

to sneeze the next four times she was near cats. Based on her experience, Caroline believes that she is

allergic to cats.

a. What is the specific information in this problem?

b. What is the general information in this problem?

c. What is the conclusion in this problem?

d. Did Caroline use inductive or deductive reasoning? Explain.

12. Consider the following statement: If M is the midpoint of ___

AB , then AB � 2AM.

a. What is the hypothesis?

b. What is the conclusion?

c. What is the truth value of the conditional statement if p is false and q is false? Explain.

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End of Chapter Test PAGE 3

Name ________________________________________________________ Date __________________________

13. Write a two column proof for the following theorem.

Given: �GBC � �HEF

�ABG � �DEH

Prove: �ABC � �DEF

B

G

C

A E

H

F

D

Statements Reasons

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End of Chapter Test PAGE 4

14. Complete the flow chart proof by writing the reason for each statement in the boxes provided.

Given: ___

AB � ___

DE ; ___

CB � ___

DF

Prove: ___

AC � ___

FE

A BC

FE D

AB � DE

CB = DF AC + CB = DF + FE

AC FE

DE = DF + FEAB = AC + CB

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Standardized Test Practice

Name ________________________________________________________ Date __________________________

1. Consider the following statement:

Clothes that are expensive are made of better materials.

Which is the hypothesis of the statement?

a. Clothes are expensive.

b. Clothes are made of better material.

c. Clothes are not expensive.

d. Clothes last longer.

2. Which of the following statements is false?

a. A postulate is a statement that can be proven.

b. The essential difference between Euclidean geometry and non-Euclidean geometry is the nature of

parallel lines.

c. The transitive property states that “if a � b and b � c, then a � c.”

d. All right angles are congruent.

3. Which of the following is an application of the Substitution Property?

a. If m�A � m�B, then m�A � m�C � m�B � m�C.

b. m�A � m�A

c. If m�A � m�B and m�B � m�C, then m�A � m�C.

d. If m�A � 110° and m�B � 110°, then m�A � m�B.

4. Which of the following statements is false?

a. Skew lines are two or more lines that are not in the same plane.

b. A plane has infinite length, width, and depth.

c. A line has infinite length, but no depth or width.

d. Two lines are perpendicular if they intersect to form 90° angles.

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Standardized Test Practice PAGE 2

5. In the figure shown,

___ › BD bisects �ABC, and

___ › BE bisects �DBC. The measure of �EBD is 35°. What is the

measure of �ABC?

a. 35°

b. 70°

c. 90°

d. 140°

A

B C

D

E

35°

6. Two angles are complementary. The smaller angle is 35° less than the larger angle. What is the measure

of the larger angle?

a. 27.5°

b. 55°

c. 62.5°

d. 125°

7. The following two statements are true.

Tom is older than David.

David is older than Aaron.

Which conclusion can be reached by deductive reasoning?

a. Tom and Aaron are the same age.

b. Tom is older than Aaron.

c. Tom is older than David.

d. Aaron is older than Tom.

8. If the truth value of a conditional statement is false, what are the truth values of p and q?

a. p is true and q is true

b. p is true and q is false

c. p is false and q is true

d. p is false and q is false

9. Consider the following conditional statement: If the measure of an angle is 150°, then the angle is obtuse.

What does the phrase “If p is false” mean in terms of this conditional?

a. The measure of the angle is 100°.

b. The angle is acute.

c. The measure of the angle is not 150°.

d. The angle is part of a linear pair.

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Chapter 1 ● Assessments 1061

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Standardized Test Practice PAGE 3

Name ________________________________________________________ Date __________________________

10. In the figure shown, ___

AC � ___

CE , D is the midpoint of ___

CE , DE � 5, and BC � 2. What is the measure of ___

AB ?

a. 5 B ECA D

b. 7

c. 8

d. 10

11. Two angles are supplementary. The larger angle is twice as large as the smaller angle. What is the

measure of the smaller angle?

a. 30°

b. 60°

c. 90°

d. 120°

12. The measure of �A is 110°. Angle A is classified as:

a. acute

b. right

c. obtuse

d. straight

13. What conclusion can you make based on the figure shown?

a. �ACD � �BCE � �DCE

b. �ACD � �BCE � 90°

c. �ACE � �BCE

d. �ACE � �BCD A

D

C B

E

14. Jack is using a compass and straightedge to do the construction shown.

What best describes the construction Jack is doing?

a. an angle bisector

b. a perpendicular bisector

c. an incenter

d. a circumcenter

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Standardized Test Practice PAGE 4

15. The figure shows intersecting lines. Which angle pairs are vertical angles?

a. �COE and �BOD

b. �COE and �EOD

c. �EOB and �AOP

d. �AOC and �COE

P

O

A

B

E

C

D

16. The figure shows CD � AB and EF � AB. Which two reasons allow you to conclude that �ACD � �BEF?

BCA E

FD

a. Perpendicular lines intersect to form right angles. All right angles are congruent.

b. Perpendicular lines intersect to form right angles. All linear pairs are congruent.

c. Perpendicular lines intersect to form right angles. Complements of congruent angles are congruent.

d. Perpendicular lines intersect to form right angles. Vertical angles are congruent.

17. What is the name of the reason that states, “If point B is on ___

AC and between points A and C,

then ___

AB � ___

BC � ___

AC .”

a. Segment Addition Postulate

b. Addition Property

c. Congruent Supplement Theorem

d. definition of a midpoint

18. In the triangle shown, AD � AE and DB � EC. What could you use to prove that AB � AC?

a. definition of a midpoint

b. definition of congruent segments

c. Segment Addition Postulate

d. Addition Property of Equality

A

C

E D

B

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Chapter 1 ● Assessments 1063

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Standardized Test Practice PAGE 5

Name ________________________________________________________ Date __________________________

19. What is the first step in constructing the perpendicular bisector of ___

AB ?

A B

a. Place the point of the compass at point B and draw an arc between points A and B.

b. Place the point of the compass at point A and draw an arc between points A and B.

c. Place the point of the compass at point B and open the compass so that it is greater than half of the

distance from point B to point A.

d. Use your straightedge to draw a line through the intersections of the arcs.

20. An angle is 50°. Which angle has the largest measurement?

a. an angle congruent to the original angle

b. the complement of the original angle

c. the supplement of the original angle

d. the original angle

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