8. ABC is an isosceles triangle in which AB = AC; BE and CF are bisectors of <B and <C respectively. Prove that BE = CF Share with your friends Share 2 Manbar Singh answered this In ∆ABC, we have AB = AC Given⇒∠C = ∠B Angles opposite to equal sides are equal⇒12∠C = 12∠B ....1Since, BE bisects ∠B, then∠ABE = ∠EBC = 12∠BSince, CF bisects ∠C, then∠ACF = ∠FCB = 12∠CNow, from 1, we get12∠C = 12∠B ⇒ ∠ABE = ∠ACFIn ∆ABE and ∆ACF, ∠A = ∠A Common AB = AC Given∠ABE = ∠ACF Proved above⇒ ∆ABE ≅ ∆ACF ASA⇒BE = CF CPCT 1 View Full Answer
