Download SECTION 14.1 – CONGRUENCE OF TRIANGLES Two geometric

SECTION 14.1 – CONGRUENCE OF TRIANGLES
Two geometric figures are congruent if they can be superimposed so as to coincide.
congruent line segments have the same length.
congruent angles have the same measure.
4ABC is congruent to 4DEF , denoted 4ABC ∼
= 4DEF , if we have A ↔ D, B ↔ E, C ↔ F
and all corresponding sides are congruent and all corresponding vertex angles are congruent.
1. Side-Angle-Side (SAS) Congruence Property: If two sides and the included angle of a
triangle are congruent, respectively, to two sides and the included angle of another triangle,
then the triangles are congruent.
2. Angle-Side-Angle (ASA) Congruence Property: If two angles and the included side of
a triangle are congruent, respectively, to two angles and included side of another triangle,
then the two triangles are congruent.
3. Side-Side-side (SSS) Congruence Property: If three sides of a triangle are congruent,
respectively, to three sides of another triangle, then the two triangles are congruent.
4. Angle-Angle-Side (AAS) Congruence Property: If two angles and the side opposite one
of the angles of a triangle are congruent, respectively, to two angles and side opposite one of
the angles of another triangle, then the two triangles are congruent.