Chapter 4.1, Problem 10WE

(a)

To determine

To find: The triangle that is congruent to $\Delta STO$ .

Answer to Problem 10WE

  $\Delta KRO$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As, the triangles are congruent, $\Delta STO$ is congruent to $\Delta KRO$ .

Therefore, $\Delta STO\cong \Delta KRO$ .

(b)

To determine

To find: The angle that is congruent to $\angle S$ and the reason.

Answer to Problem 10WE

  $\angle S\cong \angle K$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As, $\Delta STO\cong \Delta KRO$ , its corresponding parts are also congruent.

Thus, $\angle S\cong \angle K$ .

(c)

To determine

To find: The line segment that is congruent to $\overline{SO}$ and the reason.

Answer to Problem 10WE

  $\overline{SO}\cong \overline{KO}$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As $\Delta STO\cong \Delta KRO$ , its corresponding parts are also congruent.

Thus, $\overline{SO}\cong \overline{KO}$ .

(d)

To determine

To find: The angle that is congruent to $\angle T$ and the reason. Also give reason why $\overline{ST}$ is parallel to $\overline{RK}$ .

Answer to Problem 10WE

  $<T\cong <R$

Explanation of Solution

Given Information: Consider two congruent triangles shown.

  

Calculation:

As $\Delta STO\cong \Delta KRO$ , its corresponding parts are also congruent.

So, $\angle T\cong \angle R$ .

  $\overline{ST}$ is parallel to $\overline{RK}$ because alternate interior angles cut by a transversal are equal, that is, $\angle S\cong \angle K$ and $\angle T\cong \angle R$ .