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AAS Angle, Angle, Side . Describe how to prove that two triangles are congruent using the AAS postulate. . What Is AAS Postulate .

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AAS Angle, Angle, Side

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Aas angle angle side

AASAngle, Angle, Side


Aas angle angle side

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


What is aas postulate

What Is 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.


Aas angle angle side

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


Angle angle side congruence

Angle Angle Side Congruence

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


Using aas to prove congruent triangles

Using AAS to prove Congruent Triangles

  • 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


Aas angle angle side

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


Aas angle angle side

  • 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


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