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Question # 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)

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ANSWERED To prove:The congruency of $$\displaystyle\vec{{{M}{H}}}\stackrel{\sim}{=}\vec{{{J}{O}}}$$.
Given information:
The following information has been given GJKM is a rhombus
$$\displaystyle\angle{J}{O}{G}=\angle{M}{H}{G}={90}^{{\circ}}$$ 2021-03-03
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,
$$\displaystyle\angle{G}$$ is common angle
$$\displaystyle\vec{{{M}{J}}}\stackrel{\sim}{=}\vec{{{G}{J}}}$$ (Rhombus)
$$\displaystyle\angle{J}{O}{G}=\angle{M}{H}{G}={90}^{{\circ}}$$
Thus, using virtue of similarity, we know that triangles JOG ang MHG are similar triangles.
Now,
$$\displaystyle\angle{G}$$ is common angle
Thus, we know that
$$\displaystyle\triangle{J}{O}{G}\stackrel{\sim}{=}\triangle{M}{H}{G}$$
Hence, by virtue of congruency, $$\displaystyle\vec{{{M}{H}}}\stackrel{\sim}{=}\vec{{{J}{O}}}$$