Chapter 4.7, Problem 2ST3

To determine

To prove: $\Delta MSN\cong \Delta PRQ$ in the given figure.

Explanation of Solution

Given:

The given figure is,

  

And the statement is,

  $\begin{array}{l}\Delta MPQ\cong \Delta PMN\\ \overline{MS}\cong \overline{PR}\end{array}$

As, $\Delta MPQ\cong \Delta PMN$ (given)

So, $\overline{PQ}\cong \overline{MN}\text{and }\angle \text{MPQ}\cong \angle \text{PMN}$ (by congruent part of congruent triangle)

Now, in $\Delta MSN\text{and}\Delta PRQ$

  $\overline{PQ}\cong \overline{MN}\text{and }\angle \text{MPQ}\cong \angle \text{PMN}$

Also, $\overline{MS}\cong \overline{PR}$ (given)

Therefore, by SAS postulate $\Delta MSN\cong \Delta PRQ$

Hence, it is proved that $\Delta MSN\cong \Delta PRQ$