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Question

In the following figure, ABCD is a parallelogram then
(i) AP bisects angle A
(ii) BP bisects angle B
(iii) DAP+CBP=APB

1078790_89bc952a7a304a77a0166057eb96f314.JPG

A
True
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B
False
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Solution

The correct option is A True
In a parallelogram,sum of adjacent angles=180
A+B=180 .......(1)
AP bisects A
BAP=ADAP
BP bisects B
ABP=BCBP
In ABP,
BAP+ABP+APB=180
ADAP+BCBP+APB=180
(A+B)+APB=180+DAP+CBP
(A+B)+APB=180+DAP+CBP
180+APB=180+DAP+CBP from (1)
APB=DAP+CBP

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