Chapter 2.6, Problem 11PSB

To determine

To Prove : $\overline{SX}\cong \overline{SW}$

Explanation of Solution

Given information:

  $\begin{array}{l}\overline{SZ}\cong \overline{ST}\\ \overline{XY}=\overline{VW}\end{array}$

  

  $\because$ y is midpoint of $\overline{ZX}$

  $\therefore \overline{YZ}=\overline{YX}\mathrm{....}(1)$

Similarly $\overline{VW}=\overline{TV}\mathrm{....}(2)$

  $\therefore$ from equation (1) and (2)

  $\begin{array}{l}\overrightarrow{YZ}=\overline{TV}\\ \therefore \overline{SZ}=\overline{ST}\mathrm{....}(a)\\ \overline{XZ}=\overline{VW}\mathrm{....}(b)\\ \overline{XZ}=\overline{TV}\mathrm{....}(c)\end{array}$

Add. (a)+(b)+(c)

  $\therefore \overline{SX}\cong \overline{SW}$