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11/07/2021 12:13 pm
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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
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11/07/2021 12:15 pm
AB = AC and
the bisectors of B and C intersect each other at O
(i) Since ABC is an isosceles with AB = AC
B = C
\(\frac{1}{2}\) B = \(\frac{1}{2}\) C
⇒ OBC = OCB (Angle bisectors)
∴ OB = OC (Side opposite to the equal angles are equal.)
(ii) In ΔAOB and ΔAOC,
AB = AC (Given in the question)
AO = AO (Common arm)
OB = OC (As Proved Already)
So, ΔAOB ΔAOC by SSS congruence condition.
BAO = CAO (by CPCT)
Thus, AO bisects A.