Chapter 4.2, Problem 11PSB

To determine

To Prove: to prove whether the given statement is true or false.

Answer to Problem 11PSB

True.

Explanation of Solution

Given information:

  

  $\Delta ABC\cong \Delta PQR$ , AD and PC are medians.

Calculation:

  $\Delta ABC\cong \Delta PQR$ , hence $BC=QR,AB=PQ$ and $AC=PR\mathrm{...}$ also, $\angle ABD=\angle PQS$

  $\begin{array}{l}\Rightarrow \frac{1}{2}BC=\frac{1}{2}QR.\\ \Rightarrow BD=BS\\ \therefore \Delta ABD\cong \Delta QPS\mathrm{.....}(SAS)\\ \therefore AD=PS.\end{array}$