Question

Is the below statement true?
The bisectors of the base angles of an isosceles triangles are unequal.
Answer: No
If true then enter 1 else if False enter 0

Answer 1

Given: ABC is an Isosceles triangle with AB = AC. BD bisects $\angle B$ and CE bisects $\angle C$
To find whether BD = CE or not!
$AB=AC$ (Given)
hence, $\angle B=\angle C$ (Isosceles triangle property) (I)
$\frac{1}{2}\angle B=\frac{1}{2}\angle C$
$\angle DBC=\angle ECB$ (II) (BD bisects $\angle B$ and CE bisects $\angle C$)
Now, In $△BDC$ and $△FBC$
$BC=BC$ (Common)
$\angle C=\angle B$ (From I)
$\angle DBC=\angle ECB$ (From II)
Thus, $△BDC\cong △CFB$ (ASA rule)
Hence, $BD=CE$ (By cpct)