Chapter 3.2, Problem 23PSB

To determine

To prove : The congruency of $\Delta BRS\cong \Delta BVP$ is to be proved

Explanation of Solution

Given information : The following information has been given

  $\angle R\cong \angle V$

  $\angle BST\cong \angle BTS$

S and T trisect RV

Formula used : If two angles and the side containing them in any triangles are congruent, then the triangles are said to be congruent by ASA property

Proof : We know that if S and T trisect RV, then

  $\overrightarrow{RS}\cong \overrightarrow{ST}\cong \overrightarrow{TV}$

Thus, we can say that

  $\overrightarrow{RS}\cong \overrightarrow{TV}$

Also,

  $\angle R\cong \angle V$

  $\angle BST\cong \angle BTS$

Hence, by ASA property, $\Delta BRS\cong \Delta BVP$ is proved