# Question Video: Using Triangle Congruence Criteria to Establish Congruence Mathematics • 11th Grade

Two triangles share two sides and a contained angle. Would the two triangles be congruent?

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### Video Transcript

Two triangles share two sides and a contained angle. Would the two triangles be congruent?

Let’s consider a triangle to begin to illustrate the problem. Here, we have a triangle 𝐴𝐵𝐶. Now, let’s see what a triangle that shares two sides and a contained angle with triangle 𝐴𝐵𝐶 would look like. We could say that the second triangle shares the sides 𝐴𝐵 and 𝐴𝐶. Note that because they are shared sides, that means that in the second triangle these will be the same length. We can therefore take the contained or included angle between these sides as the angle 𝐴.

We can recall the side-angle-side congruence criterion, which states that two triangles are congruent if two sides and the included angle in one triangle are congruent to the corresponding parts in the other triangle. In this case, as the sides are shared, then the two triangles would sit exactly on top of one another. But even if two triangles simply had two pairs of congruent sides and an included angle congruent, they would also be congruent.

So we can give the answer as yes, since two triangles that share two sides and a contained angle are congruent.

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