Maths / Areas Of Parallelograms And Triangles / Parallelograms on Same Base and Between Same Parallels

QUESTION
 

ABCD is a parallelogram; O is any point on AC, Through O draw PQ║AB and LM║AD. Prove that ar (DLOP) =ar (BMOQ).

EXPLANATION
Explain TypeExplanation Content
Text

Since,a diagonal of a parallelogram divides it into two Triangles of equal area.

Since, AO & OC are diagonals of a parallelogram AMOP & OQCL

ar(∆APO) = ar(∆AMO) ………..(1)

ar(∆OLC) = ar(∆OQC) ………..(2)

ar(∆ADC) = ar(∆ABC)

ar(∆APO) + ar(||gmDLOP) +ar(∆OLC) =

ar(∆AMO) + ar(||gm BMOP) +ar(∆OQC) …(3)

Subtract eq 1 & 2 from 3

ar(||gmDLOP) = ar(||gm BMOQ)

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