Question

Prove that the perpendicular bisector of the base of an isosceles triangle passes through the vertex of the triangle.please give the answer fast​

Answer 1

The perpendicular bisector of an isosceles triangle will always pass through vertex as the perpendicular being drawn bisects the angle at the vertex.

• In an isosceles triangle, the bisector of an angle is always unique.  The angle bisector, median and an altitude drawn from the vertex of an isosceles triangle will coincide.
• Thus, the perpendicular that is drawn from the vertex to the base,  would also bisect the angle which is at the vertex.  Therefore, the perpendicular bisector on the base of the isosceles triangle will always pass through the vertex of the triangle.