Question 1:
In an isosceles triangle ABC, with AB = AC, the bisectors of ∠B and ∠C intersect
each other at O. Join A to O. Show that:
(i) OB = OC (ii) AO bisects ∠A
Answer:
(i) It is given that in triangle ABC, AB = AC
∠ACB = ∠ABC (Angles opposite to equal sides of a triangle are equal)
∠OCB = ∠OBC
OB = OC (Sides opposite to equal angles of a triangle are also equal)
(ii) In ∆OAB and ∆OAC,
AO =AO (Common)
AB = AC (Given)
OB = OC (Proved above)
Therefore, ∆OAB ≅ ∆OAC (By SSS congruence rule)
∠BAO = ∠CAO (CPCT)
AO bisects ∠A.
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