Answer :

Given: ABCD is a square and PB=PD


To prove: CPA is a straight line


Proof:


∆APD and ∆APB,


DA = AB …as ABCD is square


AP = AP … common side


PB = PD … given


Thus by SSS property of congruence,


∆APD APB


Hence, we know that, corresponding parts of the congruent triangles are equal


APD = APB …(1)


Now consider ∆CPD and ∆CPB,


CD = CB … ABCD is square


CP = CP … common side


PB = PD … given


Thus by SSS property of congruence,


∆CPD CPB


Hence, we know that, corresponding parts of the congruent triangles are equal


CPD = CPB … (2)


Now,


Adding both sides of 1 and 2,


CPD +APD = APB + CPB …(3)


Angels around the point P add upto 360°


CPD +APD + APB + CPB = 360°


From 4,


2(CPD +APD) = 360°


CPD +APD = = 180°


This proves that CPA is a straight line.


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