SSS Theorem of Congruence (Side-Side-Side)

Definition: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Example: Determine if the triangles are congruent.

trianglesss2.png

Solution:

The given triangles are marked to show which parts are congruent. Using this information we can decide if the triangles are congruent.

Step 1: According to the given figure: side AB is congruent to side LM, side BC is congruent to side MK side AC is congruent to side LK

Step 2: The Side-Side-Side (SSS) Theorem of congruence tells us if three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent.

We can conclude that these triangles are congruent according to the SSS Theorem

We can write this as: ∆ABC ≅ ∆LMK, which reads “Triangle ABC is congruent to Triangle LMK”.

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