Question

ABCD is a trapezium with AB // DC. A line parallel to AC intersects AB at point M and BC at point N.
Prove that: area of Δ ADM = area of Δ ACN.

Answer 1

Given: ABCD is a trapezium.

AB || CD, MN || AC
Join C and M

We know that the area of triangles on the same base and between the same parallel lines are equal.
So Area of ΔAMD = Area of ΔAMC

Similarly, consider the AMNC quadrilateral where MN || AC.
ΔACM and ΔACN are on the same base and between the same parallel lines. So areas are equal.

So, Area of ΔACM = Area of ΔCAN
From the above two equations, we can say
Area of ΔADM = Area of ΔCAN

Hence Proved.