5-1 + 5-2 Perpendicular & Angle Bisectors & Triangle Bisectors

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment

Converse of the Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

Locus

set of points that satisfies a given condition

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle

Converse of the Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

Circumcenter

The point of concurrency for the perpendicular bisectors of a triangle, inside acute triangles, outside obtuse triangles, on the midpoint of the hypotenuse for right triangles. Equidistant from the vertices of the triangle.

Incenter

The point of concurrency for the angle bisectors of a triangle - always inside

Circumcenter Theorem

The circumcenter of a triangle is equidistant from the vertices of the triangle

Incenter Theorem

The incenter of a triangle is equidistant from the sides of the triangle