yes, because perpendicular lines always intersect. all lines intersect unless they are parallel or on separate planes (skew)
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The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
The angle bisectors always intersect inside the triangle. (This is not true for altitudes and right bisectors.)
Yes.
equalateral
No, the angle bisector of a scalene triangle actually intersects at two points, the point between the two points and the vertex formed by two lines of a scalene triangle. * * * * * On an alternative interpretation of the question, the three angle bisectors of any triangle always intersect at a point which is called the incentre.