Q. 34.8( 4 Votes )

BD and CE are bisectors of B and C of an isosceles Δ ABC with AB = BC. Prove that BD = CE.

Answer :


Given,


In isosceles Δ ABC,


BD and CE are bisectors of B and C


And,


AB = AC


To prove: BD = CE


Proof: In Δ BEC and Δ CDB, we have


B =C (Angles opposite to equal sides)


BC = BC (Common)


BCE = CBD (Since, C = B C = B BCE = CBD)


By ASA theorem, we have


Δ BEC Δ CDB


EC = BD (By c.p.c.t)


Hence, proved


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