Chapter 4.7, Problem 26WE

To determine

To proof: The TM is a median.

Answer to Problem 26WE

The TM is a median.

Explanation of Solution

Given:

The triangle is shown below:

  

Angle RTS is 90 degree. MN is the perpendicular bisector of TS .

Calculation:

Consider in triangles MNS and RTS .

  $\begin{array}{l}\angle MSN=\angle RST\left(\text{Common}\right)\\ \angle RTS=\angle MNS=90°\left(\text{Given}\right)\\ \therefore \Delta MSN\sim \Delta RST\left(\text{AA}\right)\\ \frac{MS}{RS}=\frac{NS}{TS}\\ \frac{MS}{RS}=\frac{NS}{2NS}\left(\text{perpendicular}\text{bisector}\right)\\ \frac{MS}{RS}=\frac{1}{2}\end{array}$

Thus, the TM is a median.