Question

ABCD is a square and P is the inside it show that PB=PD. prove also that CPA is a straight line. pls. tell the answers​

Answer 1

Answer:

Join AC

In triangle ABP and DCP,

AB=DC(sides of square)

angle APB=angle DPC(vertically opp. angle)

angle PAB= angle PCD (Alt. int. angle)

ABP is congruent to DCP

PB=PD(By CPCT)

angle APB=angle CPD (vertically opp angle)---(1)

angle APD=angle BCP(vertically opp angle)---(2)

Now,sum of all angle around a point is 360

<APB +<CPD+<APD +<BCP=360

<CPD+CPD+<APD+<APD=360. (using 1 and 2)

2(<CPD+<APD)=360

<CPD+<APD=180

Hence,CPA is straight line.

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