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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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Presentation Transcript
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.
slide4

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

slide7

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

slide8

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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