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 AASREVIEW 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 BC2. AD ║ EC3. 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)