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Determine whether the pair of triangles is similar. Explain your reasoning.

42
A
3 cm
5 cm
4 cm
12.5 cm
A
10 cm
7.5 cm

User T W
by
7.9k points

1 Answer

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Answer:

the triangles are similar

Explanation:

You want to know if the triangle with side lengths 3, 4, 5 cm is similar to one with side lengths 12.5, 10, 7.5 cm.

When we write the ratios of the side lengths in order from shortest to longest, we have ...

3 : 4 : 5 ⇔ 7.5 : 10 : 12.5

The latter ratios are 2.5 times (3 : 4 : 5), so we can say the sides of one triangle are proportional to the sides of the other.

The triangles are similar.

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Additional comment

We have not been given a similarity statement, so we cannot compare on the basis of the way the sides are named. We can only say that a true similarity statement could be written for these triangles.

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User QMaster
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