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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.
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Solution
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.
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