Chapter 6, Problem 16CT

To determine

To Prove: $m\angle R>m\angle T$

Explanation of Solution

Given information:

  

Consider the following data:

  $\begin{array}{l}XS>YS\hfill \\ \overline{RX}\cong \overline{TY}\hfill \end{array}$

S is midpoint of $\overline{RT}$ .

Consider the triangles ΔRXS and ΔTYS

  $\begin{array}{l}\overline{RX}\cong \overline{TY}\hfill \\ \angle RSX\cong \angle TSY\hfill \\ \overline{RS}\cong \overline{TS}\hfill \end{array}$

Therefore, $\Delta RXS\cong \Delta TYS$ .

Since, $XS>YS$ .

Hence, $m\angle R>m\angle T$.