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  • E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]

E is the mid-point of the side AD of the trapezium ABCD with AB \parallel DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]

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Solution.
Given: ABCD is trapezium and AB\parallel DC
Constructions: Join AC which intersect EF at O

Proof: In \triangle ADC, E is the mid-point of line AD and OE \parallel CD.
By mid-point theorem, O is mid-point of AC
∴ In \triangle CBA, as O is mid-point of AC
 OF\parallel AB (mid-point theorem)
Hence again by mid-point theorem, F is the mid-point of BC.
Hence proved

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