AAS Angle, Angle, Side

1. AASAngle, Angle, Side

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

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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