Math 2 Unit 3 Worksheet 1 Name: Congruent Figures Date: Per

Math 2 Unit 3 Worksheet 1 Congruent Figures

Name:

Date:

Per:

[1-2] Each pair of polygons is congruent. Find the measures of the numbered angles.

1.

2.

[3-7] Use the diagram to the right. Complete the congruence statements.

3. AB

6. Z

4. ZY

7. B

5. BAC

[8-9] Given FOUR MANY. List each of the following. 8. Four pairs of congruent angles

9. Four pairs of congruent sides

[10-11] Can you conclude that the figures are congruent? Justify your answer.

10.

11.

Math 2 Unit 3

Worksheet 1

12. If , which of the following must be a correct congruence statement?

13. Reasoning: A student says she can use the information in the figure to prove . Is she correct? Explain in complete sentences.

[14-15] Find the values of the variables. 14.

15.

[16-17] . Find the measures of the given angles or the lengths of the given sides.

16. = + ; = 3

17. = 3 - 2; = + 6

Math 2 Unit 3

Worksheet 1

Math 2 Unit 3 Worksheet 2 Types of Triangle Congruence

Name:

Date:

Per:

[1-15] Determine if they two triangles are congruent. If yes, state the postulate that makes the triangles congruent.

If no, write, "not enough information".

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

Math 2 Unit 3

15.

Worksheet 2

16. Suppose , , and . Is congruent to ? Explain your reasoning.

[17-19] Name two triangles that are congruent by ASA.

17.

18.

19.

20. Can you prove the below triangles are congruent? Justify your answer.

[21-26] In the diagram, . Complete the statement.

21.

22.

23. 25.

24. 26.

[27-28] Find the value of x.

27.

28.

Math 2 Unit 3

Worksheet 2

Math 2 Unit 3 Worksheet 3 Triangle Congruence Proofs

1. Given: , Prove:

Name: Date:

Statements

Per: Reasons

2. Given: is the midpoint of and Prove:

Statements

Reasons

[3-6] Developing a Proof: Complete the two-column proof by filling in the blanks.

3. Given: , bisects Prove:

Statements 1) , bisects 2) 3) 4) 5)

6)

4. Given: , Prove:

Prove:

Statements 1) , 2) 3)

Reasons 1) Given 2) Definition of Perpendicular 3) 4) 5) Reflexive Property of 6) ASA

Reasons 1) Given 2) 3) AAS

Math 2 Unit 3

Worksheet 3

5. Given: , Prove:

Statements 1) 2) 3)

Reasons 1) Given 2) 3) AAS

6. Given: is the angle bisector of and Prove: Statements

1)

2)

3) 4) 5)

Reasons 1) 2) Definition of bisector 3) 4) 5) ASA

[7-9] Name a pair of overlapping congruent triangles. State the postulate which proves the two triangles congruent. 7. Given: ,

8. Given: , 9. Given: ,

Math 2 Unit 3

Worksheet 3

Math 2 Unit 3 Worksheet 3A Reflexive Property of Congruence

Name:

Date:

Per:

The reflexive property of congruence states that a segment is congruent to itself.

1. Given: ,

2. Given: ,

Prove: ________

Prove: _______

Statement

Reason

1. , 1.

2.

2.

3. ________ 3.

Statement 1.

2. 3. ________

Reason 1. Given

2. Reflexive Prop. of

3.

3. Given: , Prove: ________

Statement 1.

2.

3.

Reason 1.

2.

3.

4. Given: , Prove: ________

Statement 1.

2.

3.

Reason 1.

2.

3.

5. Given: and are right angles,

Prove: ________

Statement 1.

2.

3.

Reason 1.

2.

3.

Math 2 Unit 3

6. Given: , Prove:

Statement 1.

2.

3.

Reason 1. 2. 3.

Worksheet 3A

Math 2 Unit 3 Worksheet 3B Vertical Angles are Congruent

Name:

Date:

Per:

When two lines intersect and form and "x" shape, the vertical angles are congruent.

1. Given: AE DE, CE BE

2. Given: C D, AE BE

Prove: CEA ________

Prove: ACE ________

Statement 1.

Reason 1. Given

2.

2.Vertical Angles are

3. ________ 3.

Statement 1. ,

2.

3. ________

Reason 1.

2.

3.

3. Given: A B, Prove: ACE ________

Statement 1.

2.

3.

Reason 1.

2.

3.

5. FIND THE ERRORS

Given: ,

Prove: ABE DCE

Statement 1.

2.

Reason 1. Given

2. Vertical angles are

3.

3. AAA

Math 2 Unit 3

4. FIND THE ERRORS Given: AB , Prove: ABE CBD

Statement 1. , 2.

3.

Reason 1. Given

2. Vertical Angles are 3. SSA

6. FIND THE ERRORS

Given: DE ,

Prove: AEC BED

Statement

Reason

1. , 1. Given

2.

2. Vertical angles are

3.

3. SSS

Worksheet 3B

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