Chapter 3.8, Problem 10PSB

To determine

The congruency of $\angle PST\cong \angle PVT$ is to be proved

Explanation of Solution

Given information : The following information has been given

P is the center of the circle

  $\overrightarrow{ST}\cong \overrightarrow{VT}$

Formula used : Similar angles of congruent triangles are congruent

Proof : We know that PS and PV are the radius of the circle. Thus, we can say that

  $\overrightarrow{PS}\cong \overrightarrow{PV}$

Also,

  $\overrightarrow{ST}\cong \overrightarrow{VT}$

And,

  $\overrightarrow{PT}\cong \overrightarrow{PT}$ (common chord)

Now, we can say that $\Delta PST\cong \Delta PVT$ by SSS rule

Thus, for congruent triangle, we can say that

  $\angle PST\cong \angle PVT$ by congruency