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ABCD is a trapezium with $A B ‖ D C$ . E and F are points on non-parallel sides AD and BC respectively such that EF is parallel to AB. Is the condition $A E E D = B F F C$ true or false?

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True

False

answer is A.

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Detailed Solution

It is given that ABCD is a trapezium with AB∥DC.
Parallel lines drawn to one side of the triangle intersect the other two sides at distinct points.
It has been given that AB∥DC & EF∥DC, therefore we can write that

A B ∥ E F ∥ D C

Let us join AC which intersects EF at G.
In

Δ A D C

, we apply the Thales theorem.

E G ∥ D C A E E D = A G G C ...... 1

Similarly, in

Δ A B C

A B ∥ G F

Therefore,

B F F C = A G G C ...... 2

From (1) & (2),

A E E D = B F F C

Hence,

A E E D = B F F C

is proved.
Therefore, the given statement is true.
Hence, the correct option is 1.

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