in an isosceles triangle ABC with AB=AC the bisectors of angle B and angle C intersect each other at O .join A to O.show that:
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in an isosceles triangle ABC with AB=AC the bisectors of angle B and angle C intersect each other at O .join A to O.show that:
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Answer:
In △ABC, we have
AB=AC
⇒∠C=∠B ∣ Since angles opposite to equal sides are equal
⇒
2
1
∠B=
2
1
∠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
Step-by-step explanation:
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