Chapter 7.2, Problem 1CYP

To determine

To list: The all pairs of congruent angles, and write a proportion that relates the corresponding for each pair of similar polygons.

Answer to Problem 1CYP

The congruent angles are, $\angle N\cong \angle U$ , $\angle P\cong \angle V$ , $\angle Q\cong \angle S$ , and $\angle R\cong \angle T$ , and proportion is $\frac{NP}{UV}=\frac{PQ}{VS}=\frac{QR}{ST}=\frac{RN}{TU}$ .

Explanation of Solution

Given:

It is given that $NPQR\sim UVST$ .

Calculation:

The order of vertices in a similarity statement identifies the corresponding angles and sides. It is given that $NPQR\sim UVST$ , one could take the corresponding angles and set them congruent to each other.

Since the corresponding sides of similar triangles are proportional to each other, one could write a proportion that relates the corresponding sides to each other.

Congruent angles are, $\angle N\cong \angle U$ , $\angle P\cong \angle V$ , $\angle Q\cong \angle S$ , and $\angle R\cong \angle T$ .

Proportions is, $\frac{NP}{UV}=\frac{PQ}{VS}=\frac{QR}{ST}=\frac{RN}{TU}$ .

Therefore, the congruent angles are, $\angle N\cong \angle U$ , $\angle P\cong \angle V$ , $\angle Q\cong \angle S$ , and $\angle R\cong \angle T$ , and proportion is $\frac{NP}{UV}=\frac{PQ}{VS}=\frac{QR}{ST}=\frac{RN}{TU}$ .