Chapter 7.2, Problem 6PSA

To determine

To prove : The congruency of $\overrightarrow{MH}\cong \overrightarrow{JO}$ .

Explanation of Solution

Given information : The following information has been given

GJKM is a rhombus

  $\angle JOG=\angle MHG={90}^0$

Formula used : By the virtue of similarity, if any two angles of the triangles are congruent, the third one will also be congruent

Proof : In triangles JOG and MHG,

  $\angle G$ is common angle

  $\overrightarrow{MJ}\cong \overrightarrow{GJ}$ (Rhombus)

  $\angle JOG=\angle MHG={90}^0$

Thus, using virtue of similarity, we know that triangles JOG ang MHG are similar triangles.

Now,

  $\angle G$ is common angle

Thus, we know that

  $\Delta JOG\cong \Delta MHG$

Hence, by virtue of congruency, $\overrightarrow{MH}\cong \overrightarrow{JO}$