Question

1. give the ratios for the corresponding sides of the given triangles. are the triangles similar? ______ explain. ______ 22 in 32 in 34 in 17 in 16 in 11 in

Explanation:

Step1: Identify corresponding sides

First, we match the sides of the two triangles. Let's assume the sides of the first triangle are 22 in, 32 in, 34 in and the second are 11 in, 16 in, 17 in. So corresponding sides are (22, 11), (32, 16), (34, 17).

Step2: Calculate the ratios

For the first pair: $\frac{22}{11} = 2$
For the second pair: $\frac{32}{16} = 2$
For the third pair: $\frac{34}{17} = 2$

Step3: Check similarity

Triangles are similar if the ratios of corresponding sides are equal. Since all three ratios are 2 (equal), the triangles are similar by the SSS (Side - Side - Side) similarity criterion.

Answer:

The ratios of corresponding sides are $\frac{22}{11}=2$, $\frac{32}{16}=2$, $\frac{34}{17}=2$. The triangles are similar because the ratios of their corresponding sides are equal (by SSS similarity criterion).