Proving Triangles Congruent—ASA, AAS - Weebly

NAME

DATE

PERIOD

4-5 Study Guide and Intervention

Proving Triangles Congruent--ASA, AAS

ASA Postulate The Angle-Side-Angle (ASA) Postulate lets you show that two triangles

are congruent.

ASA Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Example Write a two column proof.

"

#

Given: A-B- C--D-

CBD ADB

Prove: ABD CDB

Statements

Reasons

%

$

1. A-B- C--D-

1. Given

2. CBD ADB

2. Given

3. ABD BDC

3. Alternate Interior Angles Theorem

4. BD = BD

4. Reflexive Property of congruence

5. ABD CDB

5. ASA

Exercises

PROOF Write the specified type of proof.

1. Write a two column proof.

2. Write a paragraph proof.

V

R

T

U

S

Given:

S T is

V, the midpoint

of

S-V-

Prove: RTS UTV

B

D

A

C

E

Given: C--D- bisects A-E-, A-B- C--D- E BCA

Prove: ABC CDE

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 4-5

Chapter 4

31

Glencoe Geometry

NAME

DATE

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4-5 Study Guide and Intervention (continued)

Proving Triangles Congruent--ASA, AAS

AAS Theorem Another way to show that two triangles are congruent is the Angle-

Angle-Side (AAS) Theorem.

AAS Theorem

If two angles and a nonincluded side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

You now have five ways to show that two triangles are congruent.

? definition of triangle congruence

? ASA Postulate

? SSS Postulate

? AAS Theorem

? SAS Postulate

Example In the diagram, BCA DCA. Which sides

are congruent? Which additional pair of corresponding parts needs to be congruent for the triangles to be congruent by

A

the AAS Theorem?

Aa-nC-glesA-cC-anbnyotthbeeRe1fleaxnidveP2r, obpeecratuysoefA-cCo-nwgrouueldncbee.

The the

congruent included side.

If B D, then ABC ADC by the AAS Theorem.

B

1 2

C

D

Exercises PROOF Write the specified type of proof.

1. Write a two column proof. Given: B--C- E-F- AB = ED C F Prove: ABD DEF

"

#

$

%

&

'

2. Write a flow proof.

S

Given: S U; T-R- bisects STU.

R

T

Prove: SRT URT

U

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 4

32

Glencoe Geometry

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