Question

In a quadrilateral ABCD, AB = AD and CB = CD.
AC bisects $\angle$ BAD

Determine True or False

• A. True
• B. False

Answer 1

The correct option is A True

In $△AOB$ and $△AOD$

$AB=AD$ (given).

$\angle BAD=\angle DAO$ ($AC$ bisects $\angle A$).

$AO=AO$ (common).

$\therefore △AOB\cong △AOD$ ($SAS$ congruence rule).

$DO=BO⟶\left(1\right)$

$\angle AOD=\angle AOB$

$\therefore \angle AOD+\angle AOB=180°$

$\therefore \angle AOD+\angle AOB=90°⟶\left(2\right)$

From $\left(1\right)$ and $\left(2\right),$

$AC$ is the perpendicular bisector of $BD.$

$\therefore AC$ bisects $\angle BAD.$

The statement is true.