| A | B |
|---|
| Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment |
| Perpendicular Bisector Converse | If a point is equidistant from the endpoints of a segment, then if lies on the perpendicular bisector of the segment. |
| Angle Bisector Theorem | If a point is on the bisector of an angle, then it is equidistant from two sides of the angle |
| Angle Bisector Converse | If a point is in the interior of an angle and equidistant from the sides of an angle, then it lies on the bisector of the angle. |
| Median | is a segment whose endpoints are a vertex and the midpoint of the opposite side |
| Perpendicular Bisector | is a segment that is part of a perpendicular bisector of one of the sides |
| Angle Bisector | is a segment that bisects one of the angles of the triangle |
| Altitude | is a segment from a vertex that is perpendicular to the opposite side or to the line containing the opposite side. An altitude of a triangle can be inside or outside of a triangle |
| Concurrent | intersecting at a single point |
| Circumcenter | is equidistant from the vertices of the triangle. Intersection of the perpendicular bisectors. |
| Incenter | Intersection of the angle bisectors. |
| Centroid | intersection of the medians |
| Orthocenter | intersection of the altitudes |
| Midsegment Theorem | The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half its length. |
| Theorem 5.10 | If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side. |
| Theorem 5.11 | If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle. |
| Triangle Inequality Thm | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
| Hinge Theorem | If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger that the included angle of the second, then the third side of the first is longer than the third side of the second. |
| Converse of Hinge Theorem | If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second. |
| Exterior Angle Inequality Thm | The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. |
