# SAS Congruence (Side-Angle-Side Congruence)

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

## Postulate

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

Start from the given statement.

Two column proof

*P* is the midpoint of *AD*.

So *AP* ≅ *AD*.

(blue segments)*P* is the midpoint of *BC*.

So *BP* ≅ *PC*.

(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*.