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 we are given the lengths of all of the sides in both triangles. Therefore, we can compare the ratios of the corresponding sides. To identify them we can use the side lengths.
Let's find and simplify the ratios!
rccccc
Shortest Sides: &JK/QR & = & 32/22 & = & 16/11 [0.8em]
Longest Sides: &JL/PQ & = & 60/40 & = & 3/2 [0.8em]
Remaining Sides: &LK/PR & = & 45/30 & = & 3/2
As we can see, only two of the ratios are equal. Therefore, the corresponding sides are not proportional and the given triangles are not similar.
