Chapter 2.6, Problem 1PSA

To determine

To Prove: $\angle KMO\cong \angle STV$

Explanation of Solution

Given information: $\angle KMR\cong \angle VTW$

  

  $\because \overline{MR}\&\overline{MP}$ Trisect $\angle KMO$

  $\therefore \angle OMP=\angle PMR=\angle RMK\mathrm{....}(1)$

  $\because \overline{TX}\&\overline{TW}$ Trisect $\angle STV$

  $\begin{array}{l}\because \angle STX=\angle XTW=\angle WTV\mathrm{....}(2)\\ \because \angle KMR\cong \angle VTW\mathrm{...}(given)\end{array}$

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

  $\begin{array}{l}\angle OMP=\angle PMR=\angle RMK=\angle STX=\angle XTW=\angle WTV\\ \therefore \angle KMO\cong \angle STV\end{array}$