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Compare the ratios of corresponding sides. Remember, compare the longest side with the longest side and the shortest side with the shortest side.
Are the Triangles Similar? Yes.
Similarity Statement: â–ł IJK ~ â–ł HFG
Explanantion: See solution.
Let's review the theorems that can help us prove that two 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