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. $\Delta ABC\cong \Delta OBC$
• C. $\Delta ABC\text{is not congruent to}\Delta OBC$
• 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

$\Delta ABC\text{is not congruent to}\Delta OBC$

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

In $\Delta$ ABC and $\Delta$OBC,

AB = AC and OB = OC

BC = BC (common side)

However, (AB, AC) $\ne$ (OB, OC)

Hence, $\Delta$ ABC and $\Delta$OBC are not congruent.