Question

The triangles below are similar. Triangle X Y Z. Side X Z has a length of 12, Z Y is 16, Y X is 14. Triangle R Q S. Side R Q is 3.5, Q S is 4, S R is 3. Which similarity statement expresses the relationship between the two triangles?

Answer 1

SSS

Explanation:

We are given a triangle XYZ with side lengths 12, 14, and 16. We are also given another triangle RQS with side lengths 3, 3.5, and 4. In order to see if they're similar, we must check whether corresponding sides have the same ratio.

The shortest side of each triangle correspond to each other; the same can be said about the medium-length sides and the longest sides. In other words, XZ = 12 corresponds with SR = 3; YX = 14 corresponds to RQ = 3.5; and ZY = 16 corresponds to QS = 4. Let's find the common ratio:

XZ / SR = 12 / 3 = 4

YX / RQ = 14 / 3.5 = 4

ZY / QS = 16 / 4 = 4

Thus, since the ratios are all 4, we can say that the two triangles are similar by the SSS (side-side-side) Similarity Theorem.

Hope this helps!

Answer 2

Triangle XYZ is similar to Triangle RQS

Explanation:

Triangle XYZ is similar to Triangle RQS

XZ/SR = 12/3 = 4

ZY/QS = 16/4 = 4

YX/RQ = 14/3.5 = 4

similar figures have all corresponding sides in the same ratio