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Question

The parallel sides of a trapezium are a and b respectively. The line joining the midpoints of its nonparallel sides will be

(a) 12(ab)

(b) 12(a+b)

(c) 2ab(a+b)

(d) ab

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Solution

The correct option is (b) 12(a+b)


Given: The parallel sides (AB and CD) of the given trapezium are of length a and b.

A line joining the midpoints of the non-parallel sides of a trapezium will always be parallel to the parallel sides of the trapezium

i.e. EFABCD

In ADB, we have

E is the midpoint of AD, and EGAB [EFAB]

By Converse of midpoint theorem, G will midpoint of BD. and EG=12AB

i.e. EG=12b(i)

In DBC, we have

G is the midpoint of BD and F is the midpoint of BC.

By midpoint theorem, GFCD, and GF=12CD

i.e. GF=12a(ii)

On adding eq.(i) and (ii), we get

EG+GF=12b+12a

EF=12(a+b)

Hence,the line joining the midpoints of its nonparallel sides is equal to 12(a+b).


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