SAS Theorem of Congruence (Side-Angle-Side)

Definition: If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

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Example: Determine if the triangles are congruent.

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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 AC is congruent to side RQ,
side AB is congruent to side RS,
Angle A is congruent to Angle R.

Step 2: The Side-Angle-Side (SAS) Theorem of Congruence tells us if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

We can conclude that these triangles are congruent according to the SAS Theorem. We can write this as:

∆ABC ≅ ∆RSQ, which reads “Triangle ABC is congruent to Triangle RSQ”.

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