Chapter 3.7, Problem 16PSB

To determine

To prove : $\text{ΔWRS}$ is isosceles.

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{PR}\cong \overrightarrow{ST}$

  $\overrightarrow{NP}\cong \overrightarrow{VT}$

  $\angle P\cong \angle T$

Formula used : Similar angles of congruent triangles are congruent

Proof : We are given the information that

  $\overrightarrow{PR}\cong \overrightarrow{ST}$

Now, we add RS on both sides. Thus, simplifying it further, we get

  $\overrightarrow{PS}\cong \overrightarrow{RT}$

Also, we know that

  $\overrightarrow{NP}\cong \overrightarrow{VT}$

  $\angle P\cong \angle T$

Now, by SAS property of congruency we can say that

  $\Delta PNS\cong \Delta TVR$

Also, we know that similar angles of congruent triangles are congruent. Thus, we can say that in the triangles PNS and TVR,

  $\angle R\cong \angle S$

Now, in $\Delta WRS$ , we can say that

  $\angle R\cong \angle S$

Thus, if two angles are congruent in a triangle, then it is said to be an isosceles triangle.

Hence, proved that $\text{ΔWRS}$ is isosceles