Question

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
\(\displaystyle\angle{J}{O}{G}=\angle{M}{H}{G}={90}^{{\circ}}\)

Answer 1

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, \(\displaystyle\vec{{{M}{H}}}\stackrel{\sim}{=}\vec{{{J}{O}}}\)