SAS Congruence (Side-Angle-Side Congruence)

SAS Congruence (Side-Angle-Side Congruence)

How to solve SAS congruence problems: postulate, example and its solution (proof).

Postulate

SAS Congruence: If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then those two triangles are congruent.

If two sides and the included angle of a triangle
are congruent to
the two sides and the included angle of another triangle,
then those two triangles are congruent.

Example

Given: P is the midpoint of line segment AD and line segment BC. Prove: triangle ABP is congruent to triangle DCP.

Start from the given statement.

Two column proof

P is the midpoint of AD.
So APAD.
(blue segments)

P is the midpoint of BC.
So BPPC.
(red segments)

APB and ∠DPC are vertical angles.
So m∠APB ≅ m∠DPC.

Two sides and the included angle of △ABP
are congruent to
two sides and the included angle of △DCP.

Then, by the SAS congruence postulate,
ABP ≅ △DCP.