Question

which type of triangle will always have a perpendicular bisector that is also an angle bisector?
o right
o scalene
o obtuse
o equilateral

Explanation:

In an equilateral triangle, all angles are \(60^{\circ}\). The perpendicular bisector of a side also bisects the opposite angle (as all angles are equal and the triangle is highly symmetric). In an obtuse triangle, this property does not always hold. In a scalene triangle, sides and angles are all of different measures, so a perpendicular bisector is not necessarily an angle - bisector. In a right - angled triangle (non - isosceles), the perpendicular bisector of a non - hypotenuse side is not an angle bisector. But in an equilateral triangle, due to its symmetry (all sides equal, all angles equal), the perpendicular bisector of a side is also an angle bisector.

Answer:

equilateral