SSS Congruence

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

Postulate

Postulate

For two triangles,
if three sides of each triangle are congruent,
then those two triangles are congruent.

This is the SSS congruence postulate.
(Side-Side-Side congruence)

Example

Example

Solution

To write a two-column proof,
make a two-column form like this.

Start from the given statement:
ABAD.

Use the other given statement:
C is the midpoint of BD.

C is the midpoint of BD.

Then, by the definition of a midpoint,
BCCD.

AC is congruent to itself:
ACAC.

This is the reflexive property.

For △ABC and △ADC,
three sides of each triangle are congruent.

ABAD
BCCD
ACAC

Then, by the SSS congruence postulate,
△ABC and △ADC are congruent.

You found the Prove statement
△ABC ≅ △ADC.

So close the two-column form
by drawing the bottom line.

This is the proof of the example.