Chapter 4.5, Problem 25HP

To determine

To prove: $\Delta PVA\cong \Delta SVT$

Explanation of Solution

Given information: The information is given in the following diagram.

  

Proof: The flow proof is given below.

  $\begin{array}{l}\underset{ASA}{\Delta PTM\cong \Delta SQR}\to \underset{CPCTC}{\overline{PT}\cong \overline{QS}}\\ \downarrow \\ \underset{Given}{\overline{PT}\parallel \overline{QS}}\to \underset{\_}{\underset{CPCTC}{\overline{PT}\cong \overline{QS}}}\\ \downarrow \downarrow \\ \underset{Alternatingangles}{\angle PQV\cong \angle STV}\to \underset{ASA}{\Delta PVA\cong \Delta SVT}\\ \underset{Alternatingangles}{\angle QPV\cong \angle TSV}\to \end{array}$