AAS Theorem of Congruence (Angle-Angle-Side)

Definition: If two angles and the side opposite one of them in a triangle are congruent to the corresponding parts in another triangle, then 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 YX,
angle A is congruent to angle Y
angle B is congruent to angle Z

Step 2: The Angle-Angle-Side (AAS) Theorem of congruence tells us if two angles and the side opposite one of them in a triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.

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

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

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