Does a bisector create two new similar triangles?

Question

Triangle A has a bisector. That bisector creates triangle B and triangle C. Will triangles B and C be similar?

If A is a equilateral triangle then yes, but what if it's not?

Answer 1

The answer is YES and NO:

When $\triangle ABC$ is isosceles triangle, $\triangle ABD, \triangle ACD$ are similar (AD is the bisector of $\angle BAC$, and $\angle ABD=\angle ACD$).

When $\triangle ABC'$ is scalene triangle, $\triangle ABD', \triangle AC'D'$ are not similar, (AD' is the bisector of $\angle BAC$, $\angle AC'D' > \angle ACD' =\angle ABD'$ ).