CH. 4-3: PROVING TRIANGLES CONGRUENT: ASA AND AAS

Mr. Schaab’s Geometry ClassOur Lady of Providence Jr.-Sr. High

School2015-2016

ASA – Angle-Side-Angle Angle-Side-Angle (ASA) Congruence

Theorem: 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.

▲ABC ≅ ▲DEF ▲QPR ≅ ▲RSQ

AAS – Angle-Angle-Side Angle-Angle-Side (AAS) Congruence

Theorem: If two angles and a non-included side of one

triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.

▲ABC ≅ ▲DEF ▲REN ≅ ▲RVN

When AAS can NOT be used:

Because the angles are marked in a different order, the congruent side in ▲KLM does not correspond to the congruent side in ▲UTS.

In other words, in the first triangle the marked side is across from the angle with two arcs, and in the second triangle the marked side is across from the angle with one mark. The two sides do NOT correspond! Look carefully!