Proving Triangles Congruent At the end of this lesson, you should be able to prove two triangles are congruent by using ASA and AAS Postulates.

Proving Congruent Triangles: Recall, to prove triangles congruent, we used the following postulates:  __________ SSS SAS AAA SSA/AAS

Angle-Side-Angle Postulate If two angles and the included side of one triangle correspond and are congruent to two angles and the included side of another triangle, then the two triangles are congruent. (ASA Postulate) The included side means the side “_______________” two angles.

In which picture could you use ASA to show the two triangles are congruent?

Proving ∆s Congruent Using ASA. T G O A StatementReason

Proving ∆s Congruent Using ASA E M N W O StatementReason

Challenge T E A M Given: Parallelogram TEAM Prove: ∆ TAM ≡ ∆ MET StatementReason

Angle-Angle-Side Theorem If two angles and a non-included side of one triangle correspond and are congruent to the two angles and the non-included side of another triangle, then the two triangles are congruent. (AAS) (AAS)

In which picture could you use AAS to show the two triangles are congruent?

Proving ∆s Congruent Using AAS G O A T S Hint: Use numbers or a single letter to name relevant angles.

StatementReasons

Final Checks for Understanding 1.Name four ways to prove that two triangles are congruent. 2.What does it mean to be an included side?...an included angle? 3. How can you justify drawing a diagonal between two vertices in a parallelogram?