Question

The alongside figure shows a parallelogram ABCD in which AE = EF = FC.

Prove that:

1. DE is parallel to FB
2. DE = FB
3. DEBF is a parallelogram.

Answer 1

Construction: 

Join DF and EB

Join diagonal BD

Since diagonals of a parallelogram bisect each other.

∴ OA = OC and OB = OD

Also, AE = EF = FC

Now, OA = OC and AE = FC

⇒ OA - AE = OC - FC

⇒ OE = OF

Thus, in quadrilatreal DEFB, bisect each other.

OB = OD and OE = OF

⇒ Diagonals of a quadrilateral DEFB bisect each other.

⇒ DEFB is a parallelogram.

⇒ DE is parallel to FB

⇒ DE = FB                   ...(Opposite sides are equal)