Q. 124.3( 10 Votes )

# ABCD is a paralle

Answer :

To Prove: BF = BC

Given: AD is produced to E, DE = DC

EC is produced to meet AB in F.

Concept Used:

Opposite sides of a parallelogram are equal.

ASA Congruence: The ASA rule states that. If two angles and the included side of one triangle are equal to two angles and included a side of another triangle, then the triangles are congruent.

Diagram: Explanation:

In Δ ACE, D, and O are mid points of AE and AC respectively.

DO||EC

OB||CF

AB = BF ….(i)

DC = BF [ AB = DC as ABCD is a parallelogram]

In Δ’s EDC and CBF, we have

DC = BC

EDC = CBF

and ECD = CFB

So, by ASA congruence criterion, we have

ΔEDC ΔCBF

DE = BC

DC = BC

AB = BC

BF = BC [ AB = BF from (i)]

Hence, Proved.

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