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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

AASAngle, Angle, Side



What is aas postulate
What Is the AAS postulate. 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 the AAS postulate.

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 the AAS postulate. 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 the AAS postulate. 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: the AAS postulate. 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

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