If ABCD is a parallelogram, then prove that ar(Δ ABD) = ar(Δ BCD) =

1.	If ABCD is a parallelogram, then prove that ar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC) = ar(Δ ACD) = 1/2 ar(\|\|gm ABCD)
Answer» ABCD is a parallelogram. When we join the diagonal of parallelogram, it divides it into two quadrilaterals. Step 1: Let AC is the diagonal, then, Area (ΔABC) = Area (ΔACD) = 1/2(Area of \|\|gm ABCD) Step 2: Let BD be another diagonal Area (ΔABD) = Area (ΔBCD) = 1/2( Area of llgm ABCD) Now, From Step 1 and step 2, we have Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = 1/2(Area of llgm ABCD) Hence Proved.

If ABCD is a parallelogram, then prove that ar(Δ ABD) = ar(Δ BCD) = ar(Δ ABC) = ar(Δ ACD) = 1/2 ar(||gm ABCD)

Answer»

ABCD is a parallelogram.

When we join the diagonal of parallelogram, it divides it into two quadrilaterals.

Step 1: Let AC is the diagonal, then, Area (ΔABC) = Area (ΔACD) = 1/2(Area of ||gm ABCD)

Step 2: Let BD be another diagonal

Area (ΔABD) = Area (ΔBCD) = 1/2( Area of llgm ABCD)

Now,

From Step 1 and step 2, we have

Area (ΔABC) = Area (ΔACD) = Area (ΔABD) = Area (ΔBCD) = 1/2(Area of llgm ABCD)

Hence Proved.