Question

If $△ABC$ is an equilateral triangle. AO, BO and CO are angle bisectors, then ______.

• A. AO = BO = CO
• B. AO = AC
• C. $△AOC\cong △COB\cong △BOA$
• D. $△AOC≆△COB≆△BOA$

Answer 1

Answer: (A), (C)

The correct options are
A AO = BO = CO
C $△AOC\cong △COB\cong △BOA$

Given: AO, BO, CO are angle bisectors,
$△ABC$ is equilateral$\Rightarrow$each angle is equal to 60°.

In $△AOC,△COB,△BOA$
$\angle OAC=\angle OAB=30°$ ( AO is the angle bisector)
Similarily $\angle ABO=\angle CBO=30°$
$\angle ACO=\angle OCB=30°$
AC = CB = BA .... (Equilateral triangle - given)

So, by ASA criteria,

$△AOC\cong △COB\cong △BOA$
$\Rightarrow AO=BO=CO$ .... (corresponding parts of congruent triangles)