Chapter 4 Practice Test Geometry

Multiple Choice

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

____1.Use the information given in the diagram. Tell why and

a. / Reflexive Property, Given
b. / Transitive Property, Reflexive Property
c. / Given, Reflexive Property
d. / Reflexive Property, Transitive Property

____2.

a. / / b. / / c. / / d. /

____3.The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to scale.

a. / 4 / b. / 5 / c. / 3 / d. / 38

____4.Given and , find the length of QS and TV.

a. / 2 / b. / 9 / c. / 8 / d. / 20

____5.Given and , find and

a. / 22 / b. / 11 / c. / 10 / d. / 25

____6.Justify the last two steps of the proof.

Given: and

Prove:

Proof:

1. / 1. Given
2. / 2. Given
3. / 3.
4. / 4.
a. / Symmetric Property of ; SSS / c. / Reflexive Property of ; SSS
b. / Reflexive Property of ; SAS / d. / Symmetric Property of ; SAS

____7.State whether and are congruent. Justify your answer.

a. / yes, by either SSS or SAS
b. / yes, by SSS only
c. / yes, by SAS only
d. / No; there is not enough information to conclude that the triangles are congruent.

____8.Name the angle included by the sides and

a. / / b. / / c. / / d. / none of these

____9.In each pair of triangles, parts are congruent as marked. Which pair of triangles is congruent by ASA?

a. / / c. /
b. / / d. /

____10.From the information in the diagram, can you prove ? Explain.

a. / yes, by ASA / c. / yes, by SAS
b. / yes, by AAA / d. / no

____11.Can you use the ASA Postulate, the AAS Theorem, or both to prove the triangles congruent?

a. / either ASA or AAS / c. / AAS only
b. / ASA only / d. / Neither

____12.Based on the given information, what can you conclude, and why?

Given:

a. / by ASA / c. / by ASA
b. / by SAS / d. / by SAS

____13.Name the theorem or postulate that lets you immediately conclude

a. / SAS / b. / ASA / c. / AAS / d. / none of these

____14.Supply the missing reasons to complete the proof.

Given: and

Prove:

a. / ASA; Substitution / c. / AAS; CPCTC
b. / SAS; CPCTC / d. / ASA; CPCTC

____15.Find the values of x and y.

a. / / c. /
b. / / d. /

____16.What is the measure of a base angle of an isosceles triangle if the vertex angle measures 38° and the two congruent sides each measure 21 units?

a. / 71° / b. / 142° / c. / 152° / d. / 76°

____17.What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 42°?

a. / 69° / b. / 84° / c. / 138° / d. / 96°

____18.Use the information in the figure. Find

a. / 32° / b. / 122° / c. / 64° / d. / 58°

____19.Find the value of x. The diagram is not to scale.

a. / / b. / / c. / / d. / none of these

____20.Find the value of x. The diagram is not to scale.

Given:,

a. / 14 / b. / 152 / c. / 16 / d. / 19

____21.The sides of an isosceles triangle have lengths , . The base has length . What is the length of the base?

a. / 18 / c. / 12
b. / 4 / d. / cannot be determined

Short Answer

22.. List the six pairs of congruent corresponding parts.

23.Based on the given information, can you conclude that ? Explain.

Given: , , and

24.Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to complete a proof.

Given:

Prove:

25.Is by HL? If so, name the legs that allow the use of HL.

26.Write the missing reasons to complete the flow proof.

Given: are right angles,

Prove:

27. Can you conclude the triangles are congruent? Justify your answer.

28.Complete the proof by providing the missing reasons.

Given: ,

Prove:

Statement / Reason
1. , , and / 1. Given
2. are right angles / 2. Definition of perpendicular segments
3. / 3. ?
4. / 4. ?
5. / 5. ?

Essay

29.Write a two-column proof.

Given: and

Prove:

30.Write a two-column proof:

Given:

Prove:

Other

31.Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence statement and explain. If no, write not possible and tell what other information you would need.

Given:

Chapter 4 Practice Test Geometry

Answer Section

MULTIPLE CHOICE (2 points each question)

1. ANS: AREF: 4-1 Congruent Figures

2.ANS:DREF:4-1 Congruent Figures

3.ANS:CREF:4-1 Congruent Figures

4.ANS:CREF:4-1 Congruent Figures

5.ANS:CREF:4-1 Congruent Figures

6.ANS:CREF:4-2 Triangle Congruence by SSS and SAS

7.ANS:AREF:4-2 Triangle Congruence by SSS and SAS

8.ANS:AREF:4-2 Triangle Congruence by SSS and SAS

9.ANS:BREF:4-3 Triangle Congruence by ASA and AAS

10.ANS:AREF:4-3 Triangle Congruence by ASA and AAS

11.ANS:AREF:4-3 Triangle Congruence by ASA and AAS

12.ANS:AREF:4-3 Triangle Congruence by ASA and AAS

13.ANS:AREF:4-3 Triangle Congruence by ASA and AAS

14.ANS:DREF:4-4 Using Congruent Triangles: CPCTC

15.ANS:DREF:4-5 Isosceles and Equilateral Triangles

16.ANS:AREF:4-5 Isosceles and Equilateral Triangles

17.ANS:DREF:4-5 Isosceles and Equilateral Triangles

18.ANS:AREF:4-5 Isosceles and Equilateral TrianglesTOP:4-5 Example 2

19.ANS:AREF:4-5 Isosceles and Equilateral TrianglesTOP:4-5 Example 2

20.ANS:AREF:4-5 Isosceles and Equilateral TrianglesTOP:4-5 Example 2

21.ANS:AREF:4-5 Isosceles and Equilateral Triangles

SHORT ANSWER ( 10 points each problem)

22.ANS:

Sides: , ,

Angles: , ,

REF:4-1 Congruent FiguresTOP:4-1 Example 1

23.ANS:

Answers may vary. Sample: Two pairs of sides are congruent, but the angle is not included. There is no SSA Congruence Theorem, so you cannot conclude with the information given.

REF:4-2 Triangle Congruence by SSS and SAS

24.ANS:

Answers may vary. Sample: Since the two triangles share the side , they are congruent by SAS. Then by CPCTC.

REF:4-4 Using Congruent Triangles: CPCTCTOP:4-4 Example 2

25.ANS:

Yes, (in each triangle)

REF:4-6 Congruence in Right TrianglesTOP:4-6 Example 1

26.ANS:

a. Definition of right triangles

b. Converse of Isosceles Triangle Theorem

c. Reflexive property

d. Angle-Angle-Side Congruence Theorem

REF:4-6 Congruence in Right TrianglesTOP:4-6 Example 2

27.ANS:

Yes, the diagonal segment is congruent to itself, so the triangles are congruent by SAS.

REF:4-1 Congruent FiguresTOP:4-1 Example 3

28.ANS:

Step 3: All right angles are congruent.

Step 4: Reflexive Property

Step 5. HL Theorem

REF:4-7 Using Corresponding Parts of Congruent TrianglesTOP:4-7 Example 2

ESSAY ( 10 points each problem)

29.ANS:

[4]

Statement / Reason
1. and / 1. Given
2. / 2. Vertical angles are congruent.
3. / 3. SAS
4. / 4. CPCTC
[3] / correct idea, some details inaccurate
[2] / correct idea, not well organized
[1] / correct idea, one or more significant steps omitted

REF:4-4 Using Congruent Triangles: CPCTC

30.ANS:

[4]

Statement / Reason
1. and / 1. Given
2. / 2. Reflexive Property
3. / 3. ASA
4. / 4. CPCTC
[3] / correct idea, some details inaccurate
[2] / correct idea, not well organized
[1] / correct idea, one or more significant steps omitted

REF:4-4 Using Congruent Triangles: CPCTC

OTHER ( 10 points each problem)

31.ANS:

Not possible; you have one pair of congruent angles and one pair of congruent sides , but you would need to know that one more pair of angles are congruent, either or , to prove the triangles congruent by AAS.

REF:4-3 Triangle Congruence by ASA and AASTOP:4-3 Example 3