Question

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

Answer 1

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