Question

State true or false:

The bisectors of the two equal angles of a triangle are equal.

• A. True
• B. False

Answer 1

The correct option is A True

given: $△ABC$, $\angle CAB=\angle CBA$, $AD$ bisects $\angle CAB$ and $BE$ bisects $\angle CBA$
To Prove: $AD=BE$
Now, in $△ADB$ and $△ABE$
$\angle DBA=\angle EAB$ (Given)
$\angle DAB=\angle EBA$ (Half angles of equal angles)
$AB=AB$ (Common)
Thus, $△ADB\cong △BEA$ (ASA rule)
Hence, $AD=BE$ (By cpct)
Thus, The bisectors of the two equal angles of a triangle are equal