A. Congruent Triangles

When two triangles have the same side lengths and angles, they are congruent. In the Warm Up, you saw that keeping some combinations of side lengths and angles constant ensured that a triangle was unique. If two triangles have one of these combinations in common, the triangles will be congruent triangles. A minimum of three pieces of information is required to show that two triangles are congruent. The congruence rules are summarized in the table below.

Congruence Condition	Description	Diagram
Side-Side-Side (SSS)	The three corresponding sides of the triangles are equal.
Side-Angle-Side (SAS)	Two corresponding sides are equal and the contained angles are equal.
Angle-Side-Angle (ASA)	Two corresponding angles are equal and the contained sides are equal.
Side-Angle-Angle (SAA)	Two corresponding angles are equal and non-contained corresponding sides are equal.

Note that in each of the pairs of triangles above, the orientation of each triangle was different. Orientation (rotations and flips) does not change size or shape.

The following are NOT congruence rules.

NOT a Congruence Rule	Description	Diagram
Angle-Angle-Angle (AAA)	The three corresponding angles of the triangle are equal.
Side-Side-Angle (SSA)	Two corresponding sides are equal and a non-contained angle is equal.

Congruent triangles can be represented using the , symbol.

When using the notation ΔABC ΔDEF, ∠A corresponds to ∠D, ∠B to ∠E, and ∠C to ∠F.