Question

The parallel sides of a trapezium are a and b respectively. The line joining the mid-points of its non-parallel sides will be
(a) $\frac{1}{2}(a-b)$
(b) $\frac{1}{2}(a+b)$
(c) $\frac{2ab}{(a+b)}$
(d) $\sqrt{ab}$

Answer 1

(b) $\frac{1}{2}\left(a+b\right)$

Explanation:

Suppose ABCD is a trapezium.
Draw EF parallel to AB.
Join BD to cut EF at M.
Now, in ∆ DAB, E is the midpoint of AD and EM || AB.
∴ M is the mid point of BD and EM = $\frac{1}{2}\left(a\right)$
Similarly, M is the mid point of BD and MF || DC.
i.e., F is the midpoint of BC and MF = $\frac{1}{2}\left(b\right)$

∴ EF = EM + MF = $\frac{1}{2}\left(a+b\right)$