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

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.