Question

Four sides of a quadrilateral are equal. Prove that its angles are bisected by its diagonals

Answer 1

i hope it will help you

Answer 2

Proved below.

Step-by-step explanation:

Given:

Here four sides of a quadrilateral are equal.

Consider a quadrilateral ABCD (all side are equal)

Construct a diagonal AC.

By SSS rule of congurency we can say that triangle ABC and triangle CDA are congruent

Therefore,  

∠ CAB = ∠ CAD

∠ ACB = ∠ ACD

∠ ABC = ∠ ADB

Hence its angle is bisected by its diagonal AC.

Similarly, construct diagonal BD.

By SSS rule of congurency we can say that triangle DAB and triangle BCD are congruent

Therefore,  

∠ ABD = ∠ DBC  

∠ ADB = ∠ BDC

∠ DAB = ∠ BCD

Hence its angle is bisected by its diagonal BD.

Hence proved.