SSS Congruence (Side-Side-Side Congruence)

SSS Congruence (Side-Side-Side Congruence)

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

Postulate

SSS Congruence: If three sides of a triangle are congruent to three sides of another triangle, then those two triangles are congruent.

If three sides of a triangle are congruent to
three sides of another triangle,
then those two triangles are congruent.

Example

Given: line segment AB is congruent to line segment AD, C is the midpoint of line segment BD. Prove: triangle ABC is congruent to triangle ADC.

Start from the given statements.

Two column proof

C is the midpoint of BD.
So BCCD.

AC is equal to itself.
So ACAC.

Three sides of △ABC are congruent to
three sides of △ADC.

Then, by the SSS congruence postulate,
ABC ≅ △ADC.