is an isosceles triangle ABC with ab = AC the bisectors of angle b and angle c intersect each other at o join a to show that over equal and a q bisects angle A ??
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(i) In △ABC, we have AB=AC⇒∠C=∠B ∣ Since angles opposite to equal sides are equal⇒ 21 ∠B= 21
∠C⇒∠OBC=∠OCB⇒∠ABO=∠ACO
…(1)⇒OB=OC ∣ Since sides opp. to equal ∠s are equal
…(2)(ii) Now, in △ABO and △ACO, we have AB=AC ∣ Given∠ABO=∠ACO ∣ From (1)OB=OC ∣ From (2)∴
By SAS criterion of congruence, we have
△ABO≅△ACO
⇒∠BAO=∠CAO ∣ Since corresponding parts of congruent triangles are equal⇒ AO bisects ∠A
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