P and Q are any two points lying on the sides DC and AD respectively o

1.	P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (PAB) = ar (BQC).
Answer» Data: P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. To Prove: ar(∆APB) = ar(∆BQC) Proof: ABCD is a parallelogram. ∴ AB \|\| DC AB = DC AD \|\| BC AD = BC Now ∆APB and ABCD are on same base AB and in between AB \|\| DC ∴ Area(∆APB) = Area ABCD) ……… (i) Similarly, ∆BQC and BADC are on the same base BC and in between BC \|\| AD. ∴ Area(∆BQC) = Area( ABCD) ………. (ii) From (i) and (ii) ∴ Area(∆APB) = Area (∆BQC).

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

Answer»

Data: P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD.

To Prove: ar(∆APB) = ar(∆BQC)

Proof: ABCD is a parallelogram.

∴ AB || DC

AB = DC

AD || BC

AD = BC

Now ∆APB and ABCD are on same base AB and in between AB || DC

∴ Area(∆APB) = Area ABCD) ……… (i)

Similarly, ∆BQC and BADC are on the same base

BC and in between BC || AD.

∴ Area(∆BQC) = Area( ABCD) ………. (ii)

From (i) and (ii)

∴ Area(∆APB) = Area (∆BQC).