Question

ABCD is a trapezium in which AB || DC. M and N are the mid-points of AD and the respectively. If AB = 12 cm, MN = 14 cm, then CD =

(a) 10 cm

(b) 12 cm

(c) 14 cm

(d) 16 cm

Answer 1

The given trapezium ABCD can be drawn as follows:

Here, .

M and N are the mid-points of AD and BC respectively.

We have,.

We need to find CD.

Join MN to intersect AC at G.

We have and a line MN formed by joining the mid-points of sides AD and BC.

Thus, we can say that

In M is the mid-point of AD and

Therefore, G is the mid point of AC

By using the converse of mid-point theorem, we get:

…… (i)

In , N is the mid point of BC and

By using the converse of mid-point theorem, we get:

…… (ii)

Adding (i) and (ii),we get:

…… (iii)

On substituting and in (iii),we get:

Hence the correct choice is (d).