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Q.

Tell whether the following statement is true or false:

In the adjoining figure, ABCD is a trapezium in which AB || DC and E is the midpoint of AD. A line segment EF || AB meets BC at F. Then F is the midpoint of BC.

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a

True

b

False

answer is A.

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Detailed Solution

Given ABCD is a trapezium in which AB || DC and E is the midpoint of AD. A line segment EF || AB meets BC at F.
In triangle DAB, E is median on AD.
Also, EO || AB.
Now, using mid-point theorem, O is median on BD.
Now in triangle BDC, O is median on BD.
Also, OF || DC.
Now, using mid-point theorem, F is median on BC.
The given statement is true.
Hence, option 1 is correct.

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