9-5 Proving Triangles Congruent by Angle-Angle-Side (AAS) C. N. Colon St. Barnabas HS Geometry HP

9.5 – Prove Triangles Congruent by AAS

9.5 – Prove Triangles Congruent by AAS REVIEW of other congruency Postulates

Try This: Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Solution: In addition to the angles and segments that are marked,  EGF  JGH by the Vertical Angles Theorem. Two pairs of corresponding angles and one pair of corresponding sides are congruent. Thus, you can use the AAS Congruence Theorem to prove that ∆EFG  ∆JHG.

Try Another One: Is it possible to prove these triangles are congruent? If so, state the postulate or theorem you would use. Explain your reasoning.

Solution: In addition to the congruent segments that are marked, NP  NP. Two pairs of corresponding sides are congruent. This is not enough information to prove the triangles are congruent.

Last One: Given: AD║EC, BD  BC Prove: ∆ABD  ∆EBC and AB  EB Plan for proof: Notice that  ABD and  EBC are congruent. You are given that BD  BC. Use the fact that AD ║EC to identify a pair of congruent angles.

Proof:Statements: 1.BD  BC 2.AD ║ EC 3.  D   C 4.  ABD   EBC 5.∆ABD  ∆EBC Reasons: 1.Given 2.Given 3.If || lines, then alt. int.  s are  4.Vertical Angles Theorem 5.ASA Congruence Postulate

HOMEWORK p. 356 #4-16 (mo4)