P is an interior point of the rectangle ABCD
prove that
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Dear Student,
Given, ABCD is a rectangle and P is an interior point in it.To Prove: ar(△PAB)+ar(△PCD)=ar(□ABCD)Proof:Since ABCD is a rectangle Therefore,AB=CD and AD=BCNow, draw a perendicular from P which meets at M on AB and at N on CD.SoArea of △PAB+Area of △PCD=12×PM×AB+12×PN×CD=12×PM×AB+12×PN×AB (since AB=CD)=12×AB(PM+PN)=12×AB×MN=12×AB×CD =12×(Area of rectangle ABCD)⇒Area of △PAB+Area of △PCD=12×(Area of rectangle ABCD)Hence Proved.
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