Question

$\text{In the given figure,}\Delta ABC\text{and}\Delta OBC\text{are both isosceles.}$
$\text{It can be concluded that:}$

• A. $\Delta AOB\cong \Delta AOC$
• B. AB = AO
• C. $\angle ABO=\angle ACO$
• D. $\Delta AOB\text{is not congruent to}\Delta AOC$

Answer 1

Answer: (A), (C)

The correct options are
A

$\Delta AOB\cong \Delta AOC$

C

$\angle ABO=\angle ACO$

$\text{In}\Delta AOB\text{and}\Delta AOC,AB=AC\text{(Sides of isosceles}\Delta ABC\text{)}.OB=OC\text{(Sides of isosceles}\Delta OBC\text{)}.AOiscommon\therefore \Delta AOB\cong \Delta AOC\text{(by SSS congruence)}$
And $\angle ABO=\angle ACO$ ( By CPCT)