Question

BE and CF are angle bisectors of equal angles ABC and ACB. Prove that BE = CF

Answer 1

given,
In triangle ABC
<ABC=<ACB
=> AC=AB(sides opp to equal angles)
=> ABC is an isosceles triangle
also,BE and CF bisects equal angles ABC and ACB ,i.e.,<ABE=<ACF

To prove:BE=CF

Proof:In ∆ABE and ∆ACF
AB=AC(given)
<ABE=<ACF(given)
<A=<A(common)
therefore,∆ABE=~∆ACF(by ASA rule)
=> BE=CF(CPCT)

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