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Question
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]
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Solution
Given: E is the mid-point of the side AD of the trapezium ABCD with AB || DC.
Also, EF || AB.
To prove: That F is the mid-point of BC.
Construction: Join AC which intersect EF at O.
Proof: In triangle ADC, E is the mid-point of AD and EF || DC. ...[Since, EF || AB and DC || AB. So, AB || EF || DC]
O is the mid-point of AC and OF || AB.
Now, OF bisect BC. ...[Converse of mid-point theorem]
Or F is the mid-point of BC.
Hence proved.
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