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ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig.). Show that F is the mid-point of BC

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Given : A trapezium ABCD with AB || DC, E is the mid-point of AD and EF || AB. 

To Prove : F is the mid-point of BC. 

Proof : AB || DC and EF || AB 

⇒ AB, EF and DC are parallel. 

Intercepts made by parallel lines AB, EF and DC on transversal AD are equal. 

∴ Intercepts made by those parallel lines on transversal BC are also equal. 

i.e., BF = FC 

⇒ F is the mid-point of BC.

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