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SSS Similarity

One triangle ...

Question

One triangle has side measures 4, 5, and 8. Another has side lengths 8, 10, and 14. Are these triangles similar? Justify your answer.

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Solution

Two triangles are similar if and only if their side lengths are proportional.

In this case, two of the sides are proportional, leading us to a scale factor of 2.

However, with the last side, 8 x 2 = 16 which is not our side length.

Thus, these pair of sides are not proportional and therefore our triangles cannot be similar.

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