The parallel sides of a trapezium are a and b respectively. The line joining the mid-points of its non-parallel sides will be

Question

Philoid · Accepted Answer

It is given in the question that,

ABCD is a trapezium

Draw EF parallel to AB and DC, and join BD intersecting EF at point M.

Now, E is the midpoint of AD and EM ∥ AB. Hence, using midpoint theorem,

EM = 1/2 AB

⇒ EM = 1/2 b

Similarly, FM = 1/2

⇒ DC = 1/2 a

EF = EM + FM

EF = 1/2 a + 1/2 b

EF = 1/2 (a + b)

∴Option B is correct