4.5 – Prove Triangles Congruent by ASA and AAS Geometry Ms. Rinaldi

Angle-Side-Angle (ASA) Congruence Postulate B If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent. If Angle Side Angle Then C A S T R

Decide whether the congruence statement is true. EXAMPLE 1 Use ASA Decide whether the congruence statement is true. Explain your reasoning. SOLUTION (A) (S) So, by ASA,

EXAMPLE 2 Use ASA Decide whether the congruence statement is true. Explain your reasoning.

Angle-Angle-Side (AAS) Congruence Postulate B If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of a second triangle, then the two triangles are congruent. If Angle Angle Side Then C A S T R

Decide whether the congruence statement is true. EXAMPLE 3 Use AAS Decide whether the congruence statement is true. Explain your reasoning. SOLUTION (A) (S) So, by AAS,

EXAMPLE 4 Use AAS Decide whether the congruence statement is true. Explain your reasoning.

State the third congruence that must be given to prove that EXAMPLE 5 Use ASA or AAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the ASA Congruence Postulate. C A F D

State the third congruence that must be given to prove that EXAMPLE 6 Use ASA or AAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the ASA Congruence Postulate. C A F D

State the third congruence that must be given to prove that EXAMPLE 7 Use ASA or AAS State the third congruence that must be given to prove that using the indicated postulate. B E Given: Use the AAS Congruence Postulate. C A F D