# <span lang="EN-US

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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