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5.2

A point is on the perpendicular bisector of a triangle if it is equidistant from the endpoints of the segment, and vice versa. Same goes with an angle bisector. [Theorums 5-2, 5-3, 5-4, 5-5]

5.3

When 3 or more lines intersect, they are concurrent. The point they meet at is called the point of concurrency.

The perpendicular bisectors of a triangle's sides meet at a point equidistant from all of the triangle's vertices, and vice versa. [Theorums 5-6, 5-7]

The point the perpendicular bisectors of a triangle's sides meet is called the circumcenter of a triangle. The point the angle bisectors of a triangle meet is called the incenter of a triangle. A circle around a triangle is circumscribed about the triangle. A circle inside a triangle is inscribed in the triangle.

A median of a triangle is a line segment which's endpoints are the triangle's vertex and the midpoint of the opposite side. The point where all 3 of the medians meet is called the centroid. The shorter side of the median divided by the centroid is 2/3 of the longer side (shorter-side = longer-side * 2/3) [Theorum 5-8]