# ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF. Then prove triangle BEC is congruent to triangle DCF.

A parallelogram is a type of quadrilateral in which the opposite sides are parallel and equal.

## Answer:

Let us explore more about parallelograms and thereby prove the given statements.

**Explanation:**

Given that ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that AB = BE and AD = DF

AB = DC [ Opposite sides of a parallelogram ]

AB = BE [ Given ]

Then, BE = DC ------------------> (I)

AD = BC [ Opposite sides of a parallelogram ]

AD = DF [ Given ]

Then, BC = DF ------------------> (II)

AD || BC ⇒ ∠DAB = ∠CBE

AB || DC ⇒ ∠DAB = ∠FDC

Then, ∠CBE = ∠FDC ------------------>( III)

From, (I), (II), and (III) statements,

In ΔBEC and ΔDCF,

- BE = DC
- BC = DF
- ∠CBE = ∠FDC

By, SAS property, ΔBEC ≅ ΔDCF