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State whether the statement is true or false.
A trapezium ABCD with AB || DC and a line parallel to AC intersects AB at X and BC at Y. Then area(ΔABX) = area(ΔACY).

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True

False

answer is A.

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Detailed Solution

Given that, trapezium ABCD with AB || DC and a line parallel to AC intersects AB at X and BC at Y.
The following figure depicts the given situation.
Question Image

ABCD is a trapezium, so AD|| BC.
Now we have

Δ A B X and Δ A C X

which lie on the same base AX and are between the same parallels AD and BC. So, we get:

a r (Δ A B X) = a r (Δ A C X)

[1]
We are given that XY|| AC.

Δ A C Y and Δ A C X

lie on the same base AC and are between the same parallel AC and XY. So, we get:

a r (Δ A C Y) = a r (Δ A C X)

[2]
From [1] and [2] we get:

a r (Δ A B X) = a r (Δ A C Y)

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