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