Question

The bisectors of the equal angles B and C of an isosceles triangle ABC meet at O. Then,
Answer: AO bisects angle A.
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given $AB=AC$

$\angle ABC=\angle ACB$

$\frac{1}{2}\angle ABC=\frac{1}{2}\angle ACB$

$\angle ABO=\angle ACO$ (OB bisects $\angle B$ and OC bisects $\angle C$)

Now, in $△AOB$ and $△AOC$,

$AO=AO$ (Common)

$AB=AC$ (Given)

$\angle ABO=\angle ACO$ (Proved above)

Thus, $△AOB\cong △AOC$ (SAS rule)

Hence $\angle BAO=\angle CAO$ (By cpct)

thus, AO bisects $\angle A$