SAS (Side-Angle-Side) Similarity 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 we are given the lengths of two sides including the right angle in both triangles. Therefore, we can compare the ratios of the corresponding sides. To identify them we can use the side lengths. Remember, compare the longer leg with the longer leg and the shorter leg with the shorter leg.
Let's find and simplify the ratios!
rccccc
Longer legs: &YZ/BC & = & 7/24.5 & = & 2/7 [1.2em]
Shorter legs: &XY/AB & = & 4/14 & = & 2/7
As we can see, both ratios are equal. Therefore, the corresponding sides are proportional, and by the SAS Similarity Theorem, the triangles are similar with the scale factor 27.
△ XYZ ~ △ ABC
