In the following figure,ABCD is a parallelogram.Prove that: 1)AP bisects angle A 2)BP bisects angle B 3)angle DAP+angle CBP = angle APB.
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Hey Mate Here Is Your Answer
In a quadrilateral ABCD
AB = AD & CB = CD
To prove: 1 AC bisect angle BAD
2 AC is perpendicular
bisector of BD
Proof: In Δ AOB & AOD
AB = AD (Given)
Angle BAD = DAD (AC bisect A)
AO = OA (Common)
Δ AOB = AOD By SAS congruence rule
OD = OB By C.P.C.T
Angle OAD = BAO By C.P.C.T
Angle AOD + AOB = 180° (sum of. angle of straight line)
Angle AOD = AOB = 90°
From eq. 1 & 2 we can say AC is perpendicular bisector of BD.
Hope It Helps You
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