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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