| A | B |
|---|
| Theorem 5-1 Triangle Midsegment Theorem | If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length. |
| Theorem 5-2 Perpendicular Bisector Theorem | If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. |
| Theorem 5-3 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. |
| Theorem 5-4 Angle Bisector Theorem | If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. |
| Theorem 5-5 Converse of the Angle Bisector Theorem | If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector. |
| Theorem 5-6 Triangle Perpendicular Bisectors | The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices. |
| Theorem 5-7 Triangle: Angle Bisectors | The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. |
| Theorem 5-8 Triangle: Medians | The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. |
| Theorem 5-9 Triangle: Altitudes | The lines that contain the altitudes of a triangle are concurrent. |
| Comparison Property of Inequality | If a = b + c and c > 0, then a > b. |
| Theorem 5-10 Triangle: Larger Angle vs. Longer Side | If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. |
| Theorem 5-11 Triangle: Longer Side vs. Larger Angle | If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. |
| Theorem 5-12 Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
