# SAS Congruence

How to use the SAS congruence to show that the given triangles are congruent: postulate, 1 example, and its solution.

## Postulate

For two triangles,

if two sides and the included angle of each triangle

are congruent,

then those two triangles are congruent.

This is the SAS congruence postulate.

(Side-Angle-Side congruence)

## Example

To write a two-column proof,

make a two-column form like this.

Start from the given statement:

P is the midpoint of AD and BC.

P is the midpoint of AD.

Then, by the definition of a midpoint,

AP ≅ PD.

P is also the midpoint of BC.

Then, by the definition of a midpoint,

BP ≅ PC.

∠APB and ∠DPC are vertical angles.

Vertical angles are congruent.

So ∠APB ≅ ∠DPC.

For △ABP and △DCP,

two sides and and the included angle of each triangle

are congruent.

AP ≅ PD

BP ≅ PC

∠APB ≅ ∠DPC

Then, by the SAS congruence postulate,

△ABP and △DCP are congruent.

You found the Prove statement

△ABP ≅ △DCP.

So close the two-column form

by drawing the bottom line.

This is the proof of the example.