SAS (Side-Angle-Side) ~ Theorem: If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.
We are asked to determine whether the given triangles are similar.
Notice that ∠ P and ∠ A are congruent. Also, we know the lengths of the sides that include these angles. Let's check whether these sides are proportional.
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PM/AN & = & 6/6 & = & 1 [0.8em]
PR/AD & = & 10/8 & = & 5/4
As we can see, the ratios are not equal. Therefore, the corresponding sides are not proportional and the given triangles are not similar.
