Chapter 5, Problem 10RP

To determine

Verify that $\overline{MP}\cong \overline{JO}$ .

Answer to Problem 10RP

  $\overline{MP}\cong \overline{JO}$ Proved.

Explanation of Solution

Given information:

  

  $HJKM$ is a parallelogram,

  $\angle JHP\cong \angle MKO$

Calculation:

  $HJKM$ is a parallelogram, $\angle JHP\cong \angle MKO$

So, opposite angles of parallelogram are congruent $\angle MKJ=\angle JHM$ ,

If the congruent angle is subtracted by congruent angle then difference is congruent,

  $\begin{array}{l}\angle OKJiscongruentto\angle PHM\\ JK=HM\left[oppositesidesareequal\right]\\ HM\left|\right|JK\end{array}$

  $\begin{array}{l}\angle MJK=\angle PMH\left[\begin{array}{l}iftwolinesare\left|\right|alandcutbytransversal\\ thentheiralternate\mathrm{int}erioranglesarecongruent\end{array}\right]\\ \Delta JKO=\Delta MHP\left[ASAproperty\right]\\ \overline{MP}\cong \overline{JO}\end{array}$

Hence, $\overline{MP}\cong \overline{JO}$ proved.