Question

ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =

(a) $\frac{3}{2}AB$

(b) 2 AB

(c) 3 AB

(d) $\frac{5}{4}AB$

Answer 1

Parallelogram ABCD is given with E as the mid-point of BC.

DE and AB when produced meet at F

We need to find AF.

Since ABCD is a parallelogram, then

Therefore,

Then, the alternate interior angles should be equal.

Thus, …… (I)

In and :

(From(I))

(E is the mid-point of BC)

(Vertically opposite angles)

(by ASA Congruence property)

We know that the corresponding angles of congruent triangles should be equal.

Therefore,

But,

(Opposite sides of a parallelogram are equal)

Therefore,

…… (II)

Now,

From (II),we get:

Hence the correct choice is (b).