Chapter 3.8, Problem 11PSB

To determine

The congruency of medians in corresponding congruent triangles is to be proved

Explanation of Solution

Given information : The following information has been given

  $\Delta ABC\cong \Delta PQR$ are the congruent triangles (lets assume)

AD and PS are the corresponding medians

Formula used : Information/data provided in the question that are used to solve this particular category of solution/solution.

Proof : We know that as AD and PS are the medians,

  $\overrightarrow{BD}\cong \overrightarrow{CD}$ , and $\overrightarrow{QS}\cong \overrightarrow{RS}$

But, due to $\Delta ABC\cong \Delta PQR$ , we know that

  $\overrightarrow{BC}\cong \overrightarrow{QR}$

Thus, we can say that

  $\overrightarrow{BD}\cong \overrightarrow{QS}$

Now, in triangles ABD and PQS, we can say that

  $\angle ABD\cong \angle PQS$

  $\overrightarrow{BD}\cong \overrightarrow{QS}$

  $\overrightarrow{AB}\cong \overrightarrow{PQ}$ ( due to congruency)

Thus, we can say that $\Delta ABD\cong \Delta PQS$

Now, by virtue of congruency we can say that

  $\overrightarrow{AD}\cong \overrightarrow{PS}$

Hence, the congruency of medians in corresponding congruent triangles is proved