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Side Side Side Postulate

Proving Congruent Triangles with SSS

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.

SSS Video

Example

In diagram 1, you can see that all 3 sides of $$ \triangle ABC$$ are congruent to the 3 sides of $$ \triangle XYZ$$.

Diagram 1
Side Side Side Postulate

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

Since these 2 triangles are con

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

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