sometimes, the altitude of isosceles triangles resting on their base and equilateral triangles are angle bisectors
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An isosceles or an equilateral triangle perhaps?
Yes, provided that the base is not one of the 2 equal sides. And it's also the perpendicular bisector of the base.
No, it's not true.
An angle bisector bisects an angle. A perpendicular bisector bisects a side.
any isosceles triangle