Side Side Side Postulate

Side Side Side postulate states that if three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent.

Example

$$\triangle ABC \cong \triangle XYZ $$

1. All 3 sides are congruent
   • ZX = CA  (side)
   • XY = AB  (side)
   • YZ = BC   (side)
2. Therefore, by the Side Side Side postulate, the triangles are congruent

Given:$$ AB \cong BC, BD$$ is a median of side AC.

Prove:$$ \triangle ABD \cong \triangle CBD $$