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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