Question

abcd is a trapezium in which abIIcd , e is the midpoint of side ad. if f is a point on side bc such that efIIcd, prove that f is midpoint of bc and ef= 1/2(ab+cd)

Answer 1

Join AC to intersect EF at O.

In triangle ACD,

Since E is the midpoint of AD and EO//CD,

So, O is the midpoint of AC. (Converse of midpoint theorem)

Therefore EO= 1/2 CD (Midpoint theorem) --------(1)

Similarly,

OF= 1/2 AB -------(2)

Adding (1) and (2),

EO+OF= 1/2 CD+ 1/2 AB

EF= 1/2 (AB+CD)