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Chapter Five
Relationships in Triangles
| Term | Definition |
|---|---|
| perpendicular bisector | In a triangle, a line segment, or ray that passes through the midpoint of a side and is perpendicular to that side. |
| concurrent lines | three or more lines intersecting at a common point. |
| point of concurrency | the point where concurrent lines intersect |
| circumcenter | the point of concurrency of the perpendicular bisectors |
| incenter | the point of concurrency for the angle bisectors |
| Perpendicular Bisector 5.1 Theorem | If a point is on a 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. |
| Circumcenter Theorem | The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. |
| 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. |
| Incenter Theorem | The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from each side of the triangle. |
| median | a triangle of a segment with endpoints being a vertex of a triangle and the midpoint of the opposite side. |
| altitude | a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side. |
| centroid | the point of concurrency of the medians of a triangle |
| orthocenter | the lines containing the altitudes of a triangle are concurrent and intersect at the orthocenter. |
| Angle Side Relationships in Triangle | If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. |
| Angle Side Relationship 5.10 | If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle. |
| Triangle Inequality Theorem | The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. |
Created by:
amgeometry
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