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AAS Angle, Angle, Side

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AASAngle, Angle, Side

Describe how to prove that two triangles are congruent using the AAS postulate.

- Angle Angle side postulate states that if two angles and its non included side of the triangle is congruent to the corresponding two angles and its non included side of the other triangle, then the two angles are congruent to each other.

EXAMPLE

D

A

B

C

E

F

< A is congruent to <D, <B is congruent to <E, and DE is congruent to AC

Therefore by the AASpostulate, triangle ABC and triangle DEFare congruent

H

L

J

Given: <L = <I, <K = <H, L J= GI

Prove: triangle LJK = IGH

G

I

K

STATEMENTS

REASONS

<L = <I, <K = <H 1. given

LJ = GI 2. given

<J = <G 3. Third < theorem

LJK = IGH 4. AAS

- Example 1

Given: AB II DE, BC = CD

Prove: triangle ABC = DEC

A

Statements

Reasons

D

B

C

AB II DE 1. given

BC = CD 2. given

<B = <D 3. Alt. Int. Angle

<A = <E 4. Alt. Int. Angle

ABC = DEC 5. AAS

E

Given: C is the midpoint of AE, AB ll DE

Prove: ABC = DEC

A

D

- Example 2

C

B

E

Statement

Reasons

1. C is the midpoint of AE 1. given

2. AC = CE 2. def. of midpoint

3. AB ll DE 3. given

4. <A = <E 4. Alt. Int. Angle

5. <B = <D 5. Alt. Int. Angle

6. ABC = DEC 6. AAS

- Example 3

A

E

F

C

D

G

Given: CD = EF, <A = <G

Prove: triangle ACD = GFE

Reasons

Statements

CD= EF 1. given

<A = <G 2. given

<C and <F right angle 3. given

<C = <F 4. right angle theorem

ACD = GFE 5. AAS