Question

In an isosceles triangle ABC, AB = AC and the bisectors of angle B
and angle C intersect each other at O. A is joined to O. Show that
(i) OB = OC (ii) AO bisects angle A.
​

Answer 1

Answer: thanks for you because are help in practise of class 9th sums

Step-by-step explanation:

Answer is in picture

Answer 2

Solution:

GivEn:

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

½ B = ½ 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.