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 bcp 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.

Explanation:

Step1: Recall similarity - ratio property

For similar triangles, the ratios of corresponding sides are equal. For $\triangle MNO\sim\triangle PQR$, we have $\frac{MN}{PQ}=\frac{NO}{QR}=\frac{MO}{PR}$. Let's use the ratio $\frac{MN}{PQ}=\frac{NO}{QR}$.
We know that $MN = 6$, $NO = 13$, and $QR = 44$.
So, $\frac{6}{PQ}=\frac{13}{44}$.

Step2: Cross - multiply to solve for PQ

Cross - multiplying gives us $13\times PQ=6\times44$.
$13PQ = 264$.
Then $PQ=\frac{264}{13}\approx20.3$.

Answer:

$20.3$