Chapter 3.2, Problem 6PSA

To determine

To prove : The congruency of $\Delta TSV\cong \Delta BSV$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{SV}$ bisects $\angle TSB$

  $\overrightarrow{VS}$ bisects $\angle TVB$

Formula used : Two triangles are congruent by Side-angle-side property, if there are two congruent sides, and the angle between them is also congruent

Proof : As $\overrightarrow{SV}$ bisects $\angle TSB$ , we can say that

  $\angle TSV\cong \angle BSV$

And, as $\overrightarrow{VS}$ bisects $\angle TVB$ , we can say that

  $\angle TVS\cong \angle BVS$

Now, we can also see that there is a common side SV between them. Hence, now we can say that

  $\angle TSV\cong \angle BSV$

  $\angle TVS\cong \angle BVS$

  $\overrightarrow{SV}\cong \overrightarrow{SV}$

Thus, now by using the SAS property as mentioned above, we can say that two triangles are congruent

Hence, proved that $\Delta TSV\cong \Delta BSV$