ABCD is a trapezium with
. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).
[Hint : Join CX.]
Solution:
We have trapezium ABCD with
. It is also given that
.
We need to prove that
We can note that
and
are on the same base AX and between the same parallels AB and CD.
(1)
(Triangles on the same base and between the same parallels are equal in area.)
Similarly,
and
are on the same base AC and between the same parallels XY and AC.
(2)
(Triangles on the same base and between the same parallels are equal in area.)
From (1) and (2), we can say that
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