# SAS Congruence

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

## Postulate

### 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

### Solution

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,
APPD.

P is also the midpoint of BC.

Then, by the definition of a midpoint,
BPPC.

∠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.

APPD
BPPC
∠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.