Question

1. triangle mno is similar to triangle pqr. find the measure of side pq. round your answer to the nearest tenth if necessary.
2. triangle scp is similar to triangle qrs. find the measure of side bg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
3. triangle bcd is similar to triangle efg. find the measure of side fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.
4. triangle ijk is similar to triangle lmn. find mn. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

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Explanation:

Step1: Recall similarity - ratio property

For similar triangles, the ratios of corresponding sides are equal. Let's take problem 13 as an example. If $\triangle MNO\sim\triangle PQR$, then $\frac{MN}{PQ}=\frac{NO}{QR}=\frac{MO}{PR}$.

Step2: Identify corresponding sides

In problem 13, assume the side - length of $MN = 6$, $NO = 13$, and $QR = 44$. We want to find $PQ$. The ratio of corresponding sides gives us $\frac{MN}{PQ}=\frac{NO}{QR}$.

Step3: Set up and solve the proportion

Substitute the known values into the proportion: $\frac{6}{PQ}=\frac{13}{44}$. Cross - multiply to get $13\times PQ=6\times44$. Then $PQ=\frac{6\times44}{13}=\frac{264}{13}\approx20.3$.

For other problems (14 - 16), the same process is followed:

1. Identify the similar triangles and the corresponding sides.
2. Set up a proportion based on the ratio of corresponding sides.
3. Cross - multiply and solve for the unknown side - length.

Answer:

For problem 13: $PQ\approx20.3$. For other problems, follow the above steps to find the lengths of the required sides.