Q4 of 49 Page 51

Suppose ABC is an isosceles triangle with AB = AC; BD and CE are bisectors of ∠B and ∠C. Prove that BD = CE.

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BD and CE are bisectors of ∠B and ∠C


∠ABD = ∠DBC


∠ACE = ∠BCE


Since Δ ABC is isosceles so


∠ABC = ∠ACB …(i)


Since BD and CE are bisectors so


2∠DBC = 2∠ECB


⇒ ∠DBC = ∠ECB …(ii)


BC = BC (Common) …(iii)


From (i) , (ii) and (iii) we can say


Δ BCE and Δ BCD are congruent to each other by A.A.S. axiom of congruency


So we can say


BD = EC (Corresponding parts of Congruent triangles)


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