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

1.	P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (ΔAPB) = ar (ΔBQC).
Answer» ΔAPB and □ABCD are on the same base AB and between the same parallel lines AB//CD. ∴ ΔAPB = 1/2 □ABCD …………… (1) Also ΔBCQ and □BCDA are on the same base BC and between the same parallel lines BC//AD. ∴ ΔBCQ = 1/2 □BCDA …………….. (2) But □ABCD and □BCDA represent same parallelogram. ∴ΔAPB = ΔBCQ [from (1) & (2)]

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

Answer»

ΔAPB and □ABCD are on the same base AB and between the same parallel lines AB//CD.

∴ ΔAPB = 1/2 □ABCD …………… (1)

Also ΔBCQ and □BCDA are on the same base BC and between the same parallel lines BC//AD.

∴ ΔBCQ = 1/2 □BCDA …………….. (2)

But □ABCD and □BCDA represent same parallelogram.

∴ΔAPB = ΔBCQ [from (1) & (2)]