1.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar(∆APB) = ar(∆BQC).

Answer»

Given: A ||gm ABCD in which P and Q are two points Q lying on the side DC and AD. 

To prove: ar(∆APB) = ar(∆BQC) 

Proof: Now ∆APB and ||gm ∆BCD have the same base AB and lie between the same parallels. [

AB || DC] 

ar(∆APB) = (1/2)ar(||gm ABCD) 

Similarly, ∆BQC and ||gm ABCD have the same base BC and lie between the same parallels (BC ||AD) 

ar(∆BQC) = (1/2)ar(||gm ABCD) …(2) 

From (1) & (2) 

ar(∆APB) = ar(∆BQC)


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