Question

Question 17
If ABCD is a quadrilateral such that diagonal AC bisects the angles A and C,then prove that AB = AD and CB = CD.

Answer 1

In a quadrilateral ABCD, diagonal AC bisects the angles A and C.

In $\Delta ADCand\Delta ABC,$
$\angle DAC=\angle BAC[\because$ AC is the bisector of $\angle Aand\angle C$
$\angle DCA=\angle BCA$ [$\because$ AC is the bisector of $\angle$ and $\angle C]$
AC = AC [common side]
$\Delta ADC\cong \Delta ABC$ [by ASA congruence rule]
AD = AB [by CPCT]
And, CD = CB [by CPCT]