Chapter 1, Problem 5RP

a.

To determine

Two segments are congruent in the diagram

Answer to Problem 5RP

  $\overline{BC}\&\overline{RT}$ are the congruent segments

Explanation of Solution

Given information:

  $\text{In }\Delta \text{ ABC and }\Delta RST$

  $\angle \text{A}=\angle S$ and $\overline{BC}=\overline{RT}$

Formula Used: Congruency of objects means objects have same size and shape.

Proof:

Since, $\overline{BC}=\overline{RT}$ , (Given)

  $\therefore$ They are congruent ( $\because$ both are of same size and have same shape and by definition)

Hence, $\overline{BC}\&\overline{RT}$ are the congruent segments.

b.

To determine

Two angles are congruent in the diagram

Answer to Problem 5RP

  $\angle \text{A \&}\angle S$ are the congruent angles

Explanation of Solution

Given information:

  $\text{In }\Delta \text{ ABC and }\Delta RST$

  $\angle \text{A}=\angle S$ and $\overline{BC}=\overline{RT}$

Formula Used: Congruency of objects means objects have same size and shape.

Proof:

Since, $\angle \text{A}=\angle S$ (Given)

  $\therefore$ They are congruent (

  $\because$ both are of same size and have same shape and by definition)

Hence, $\angle \text{A \& }\angle S$ are congruent