# To prove:The congruency of vec(MH) ~= vec(JO). Given information: The following information has been given GJKM is a rhombus /_JOG=/_MHG=90^(circ)

To prove:The congruency of $\stackrel{\to }{MH}\stackrel{\sim }{=}\stackrel{\to }{JO}$.
Given information:
The following information has been given GJKM is a rhombus
$\mathrm{\angle }JOG=\mathrm{\angle }MHG={90}^{\circ }$
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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,
$\mathrm{\angle }G$ is common angle
$\stackrel{\to }{MJ}\stackrel{\sim }{=}\stackrel{\to }{GJ}$ (Rhombus)
$\mathrm{\angle }JOG=\mathrm{\angle }MHG={90}^{\circ }$
Thus, using virtue of similarity, we know that triangles JOG ang MHG are similar triangles.
Now,
$\mathrm{\angle }G$ is common angle
Thus, we know that
$\mathrm{△}JOG\stackrel{\sim }{=}\mathrm{△}MHG$
Hence, by virtue of congruency, $\stackrel{\to }{MH}\stackrel{\sim }{=}\stackrel{\to }{JO}$