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Question

Compare and contrast a perpendicular bisector and a median of a triangle.

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Answer 1

The term perpendicular bisector can apply to any segment. It is a line that bisects that segment and is perpendicular to it.
As the term perpendicular bisector applies to triangles it refers to the perpendicular bisector of one side of the triangle. A median of a triangle, on the other hand, connects the midpoint of a side of the triangle with the opposite vertex. In the case of an isosceles triangle, the perpendicular bisector of the base and the median drawn to the base are one in the same segment. This is also true of all three sides of the equilateral triangle.
All three medians of any triangle meet in the, centroid, geometric center, or center of mass of the triangle.
All three perpendicular bisectors of a triangle meet in the circumcenter of the triangle. A circle drawn with that point as its center and passing through one of the vertices of the triangle, passes through all three vertices and circumscribes the triangle. A circumcenter of a triangle is not necessarily in the interior of the triangle.