Chapter 7.2, Problem 5PSA

To determine

To prove : The congruency of $\overrightarrow{SO}\cong \overrightarrow{TO}$ .

Explanation of Solution

Given information : The following information has been given

O is the center of the circle

  $\angle SOV=\angle TOW$

  $\angle WSO=\angle VTO$

Formula used : By the virtue of similarity, if any two angles of the triangles are congruent, the third one will also be congruent

Proof : From the given information we can say that by the virtue of similarity, triangles OWS and OVT are similar.

Now, we know that

  $\overrightarrow{OW}\cong \overrightarrow{OV}=R$

Thus, now we can say that

  $\Delta OWS\cong \Delta OVT$

Hence, for congruent triangles, we use virtue of congruency to tell us that

  $\overrightarrow{SO}\cong \overrightarrow{TO}$

Hence, the given congruency is proved