Question

ABCD and EFGD are two parallelograms and G is the midpoint of CD.Then prove that area of DPC=1/2area of EFGD

Answer 1

Answer:

Area of Δ DPC  =  Area of Parallelogram EFGD

Step-by-step explanation:

G is mid point of CD (Given)

Thus, DG = GC

Considering Δ DPG = Δ GPC ( Since both have equal bases and even the height is common as both lie in same parallel lines.)  (1)

Area of Δ DPC = Area of  Δ DPG + Area of  Δ GPC = 2 Δ DPG  ( as per 1)

Area of  Δ DPG = 1/2 Area of Δ DPC (2)

Δ DPG and Parallelogram EFGD  lie between the same parallel lines and have the same base.

Thus, area of Δ DPG  = 1/2 of area of Parallelogram EFGD (3)

Substituting (2) in (3)

1/2 Area of Δ DPC  = 1/2 of area of Parallelogram EFGD

Area of Δ DPC  =  area of Parallelogram EFGD