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 all the sides 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 longest side with the longest side and the shortest side with the shortest side.
Let's find and simplify the ratios!
rccccc
Longest Sides: &JK/FG & = & 6/9 & = & 2/3 [1.2em]
Shortest Sides: &IJ/HF & = & 4/6 & = & 2/3 [1.2em]
Remaining Sides: &KI/GH & = & 5/7.5 & = & 2/3
As we can see, all three ratios are equal. Therefore, the corresponding sides are proportional, and by the SSS Similarity Theorem, the triangles are similar.
â–ł IJK ~ â–ł HFG
