Question

suppose ABC is an isosceles triangle with AB=AC;BD and CE are bisectors of angle B and angle C. prove that BD=CE

Answer 1

since ABC is an isosceles triangle
AB=AC
angleABC= angleACB (angle opp. to equal side are equal)
angleABC/2=angleACB/2
angleDBC=angleDCB
BD=CE (side opp. to equal angle is equal)

Answer 2

BD = CE where ABC is an isosceles triangle with AB=AC; BD and CE are bisectors of ∠B and ∠C

Step-by-step explanation:

ABC is an isosceles triangle with AB=AC

BD and CE are bisectors of angle B and angle C

=> ∠ABD = ∠CBD = ∠B/2

& ∠ACE = ∠BCE = ∠C/2

∠B = ∠C  as AB = AC

=> ∠ABD =  ∠ACE

Comparing Δ ABD  & Δ ACE

AB = AC  (given)

∠A = ∠A  ( common)

∠ABD =  ∠ACE

=> Δ ABD  ≅ Δ ACE

=> BD = CE

QED

Proved

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