Question

Show that each diagonal of a rhombus bisects the angle through which it passes.

Answer 1

\[\text{ In ∆ AED and ∆ DEC }: \]
\[ AE = EC (\text{ diagonals bisect each other })\]
\[AD = DC (\text{ sides are equal })\]
\[DE = DE (\text{ common })\]
\[\text{ By SSS congruence }: \]
\[ ∆ AED \cong ∆ CED\]
\[\angle ADE = \angle CDE (\text{ c . p . c . t })\]
\[\text{ Similarly, we can prove ∆ AEB and ∆ BEC, ∆ BEC and ∆ DEC, ∆ AED and ∆ AEB are congruent to each other } . \]
\[\text{ Hence, diagonal of a rhombus bisects the angle through which it passes } . \]
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