Answer:
Keep these axioms in mind while proving this
1. If a triangle and parallelogram have same base and are between the same parallel, then area of Parallelogram=  × (Area of triangle)
2. Two parallelogram sharing the same base and if the sides parallel to the base are lying in the same line, their areas are equal.
Given: A B CD is a parallelogram and E is any point on AB . If DE produced meets CB produced at F .
Proof:
AS, A B CD is a parallelogram.
AB â•‘CD
AD â•‘CB
C F â•‘AD
Δ A D F and ║gm ABCD have same base AD and lying between the same parallels, AD ║CF.
→→Area ( Δ A D F)=  × Area (║gm ABCD)------(1)
Similarly, Δ  D E C and ║gm ABCD have same base CD and lying between the same parallels, CD ║AB.
→→Area ( Δ  D E C)=  × Area (║gm ABCD)-----(2)
From (1) and (2)
→→→→Area ( Δ A D F)=Area ( Δ DEC)
(2) Area ( Δ A D F)=  Area ( Δ DEC)
→→Area ( Δ A D F)- Area (ΔA DE)=  Area ( Δ DEC)- Area (ΔA DE)
→→Area ( Δ A E F)=Area ( Δ A D E)+Area ( Δ B E C)-Area (ΔA DE)→→[Area ( Δ  D E C)=  × Area (║gm ABCD)]→→→[ Area ( Δ  D E C)=Area ( Δ A D E)+Area ( Δ B E C)]
→→Area ( Δ A E F)=Area ( Δ B E C)
Step-by-step explanation:
