Congruent Triangles Proof Worksheet

Geometry, Unit 5 ? Congruent Triangles Proof Activity ? Part I

For each problem, do the following:

Name _________________________

a. Show the given information in the diagram (using tick marks to show congruent sides and arcs to show congruent angles)

b. Show any other congruent parts you notice (from vertical angles, sides shared in common, or alternate interior angles with parallel lines)

c. Give the postulate or theorem that proves the triangles congruent (SSS, SAS, ASA, AAS, HL)

d. Finally, fill in the blanks to complete the proof.

B

D

1.

Given:

BC DC ; AC EC

Prove:

BCA DCE

C

Statements

Reasons

1.

1.

Given

A

E

2.

2.

Vertical s Theorem

3. BCA DCE

3.

2.

Given:

JK LK ; JM LM

Prove:

KJM KLM

K

Statements

Reasons

1.

1.

2.

2.

Reflexive Prop.

3.

3.

3.

Given:

G I ; FH

bisects GFI

Prove:

GFH IFH

Statements

Reasons

1. G I ; FH

bisects GFI 1.

M

J

L

G

F

H

2.

GFH IFH

3.

2.

Def. of ___________________ I

3.

Reflexive Prop.

4.

4.

N

4.

Given:

N and Q are right angles; NO PQ

Prove:

ONP PQO

Statements

Reasons

1. N and Q are right angles 1.

O

2.

ONP and PQO are _________________ triangles

2.

Def. of right triangle

3.

3.

Reflexive Prop.

4.

NO PQ

4.

5.

5.

S

5.

Given:

ST || RU ; SR || TU

Prove:

SRT UTR

Statements

Reasons

1. ST || RU

2.

1. R

2.

If lines ||, alt. int. s

3.

SR || TU

3.

4.

SRT UTR

4.

5.

5.

6.

6.

6.

Given:

W and Y are right angles;

VX ZX ; X is the midpoint of WY

Prove:

VWX ZYX

V

Statements

Reasons

1.

W and Y are right angles

1.

2.

2.

Def. of right triangle

3.

VX ZX ; X is the midpoint of WY

3.

W

4.

4.

Def. of midpoint

5.

5.

P Q

T U

Z

X

Y

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