The given figure shows a parallelogram ABCD in which E is mid-point of AD and DL // EB. Then, BF is equal to :

1. AD

2. BE

3. AE

4. AB

By equal intercept theorem,

If a transversal makes equal intercepts on three or more parallel lines, then any other line cutting them will also make equal intercepts.

In parallelogram ABCD,

DL || EB

Since, E is mid-point of AD.

∴ AE = ED

∴ BL = LC (By equal intercept theorem)

In △ BLF and △ DLC,

⇒ ∠BLF = ∠DLC (Vertically opposite angles are equal)

⇒ BL = LC (Proved above)

⇒ ∠LBF = ∠LCD (Alternate angles are equal)

∴ △ BLF ≅ △ DLC (By A.S.A. axiom)

We know that,

Corresponding parts of congruent triangle are equal.

∴ BF = CD ………(1)

We know that,

Opposite sides of parallelogram are equal.

∴ AB = CD ………(2)

From equation (1) and (2), we get :

⇒ BF = AB.

Hence, Option 4 is the correct option.