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Question

In a quadrilateral ABCD, AB = AD and CB = CD.
AC bisects BAD
Determine True or False

A
True
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B
False
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Solution

The correct option is A True
In AOB and AOD
AB=AD (given).
BAD=DAO (AC bisects A).
AO=AO (common).
AOBAOD (SAS congruence rule).
DO=BO(1)
AOD=AOB
AOD+AOB=180°
AOD+AOB=90°(2)
From (1) and (2),
AC is the perpendicular bisector of BD.
AC bisects BAD.
The statement is true.

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