Term
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Definition
| of a segment, a ray, or even a plane that is perpendicular to the segment at its midpoint. |
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Term
| Perpendicular Bisector Theorem |
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Definition
| If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. |
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Term
| Converse of the Perpendicular Theorem |
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Definition
| If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. |
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Term
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Definition
| If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. |
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Term
| Converse of the Angle Bisector Theorem |
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Definition
| 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. |
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Term
| A perpendicular bisector of a Triangle |
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Definition
| is a line (or a segment, a ray, or a plane) that is perpendicular to a side of the triangle at the side's midpoint. |
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Term
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Definition
| When there or more lines intersect at one point |
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Term
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Definition
| The point at which they interest is called the point of concurrency. |
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Term
| Concurrency of a Perpendicular Bisector Theorem |
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Definition
| The perpendicular bisectors of the sides of the triangle are concurrent from the vertices. |
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Term
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Definition
| the point of concurrency of the perpendicular bisectors of the perpendicular bisectors of this triangle, is also called the circumcenter of the triangle. |
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Term
| Circumcenter of an acute triangle |
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Definition
| The circumcenter point is inside the triangle. |
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Term
| The circumcenter of a Right Triangle |
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Definition
| The circumcenter is on the hypotenuse |
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Term
| The circumcenter of an obtuse angle |
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Definition
| Circumcenter is outside of a triangle. |
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Term
| Angle Bisector of a Triangle |
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Definition
| An angle bisector of a triangle is a bisector of an angle of the triangle. |
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Term
| Concurrency of an Angle Bisector Theorem |
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Definition
| The bisector of the angles of triangle are concurrent at a point equidistant from the side of the triangle. |
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Term
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Definition
| The point of concurrency of the angle bisector of a triangle is called the incenter of the triangle and the incenter is always inside the triangle. t |
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Term
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Definition
| is a segment whose endpoints are a vertex and the midpoint of the opposite side. A triangle's three medians are always concurrent. |
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Term
| Concurrency of a Medians Theorem |
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Definition
| 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. |
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Term
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Definition
| is the perpendicular segment from a vertex of the triangle to the line containing the opposite side. An altitude of a triangle can be a side of the triangle. |
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Term
| Concurrency of Altitudes Theorem |
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Definition
| The lines that contain the altitudes of a triangle are concurrent |
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Term
| Orthocenter of a Triangle |
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Definition
| The lines that contain the altitudes of a triangle are concurrent at the orthocenter of the triangle. The orthocenter of a triangle can be inside, on, or outside the triangle. |
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