Question

In given figure diagonal AC of a quadrilateral, ABCD bisects the angles $\angle A$ and $\angle C$. Prove that AB = AD and CB = CD.

Answer 1

Since diagonal AC bisects the angles $\angle A$ and $\angle C$,

we have $\angle BAC=\angle DAC$ and $\angle BCA=\angle DCA$.

In triangles ABC and ADC,

we have

$\angle BAC=\angle DAC$ (given);

$\angle BCA=\angle DCA$ (given);

AC = AC (common side).

So, by ASA postulate, we have

$△BAC\cong △DAC$

$\Rightarrow$ BA = AD and CB = CD (Corresponding parts of congruent triangle).