Term
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Definition
| A segment, ray, line or plane that is perpendicular to a 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 Bisector 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 it is equidistant from the two sides of the angle. |
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Term
| Converse Of the Angle Bisector Theorem |
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Definition
| If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the bisector of the angle. |
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Term
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Definition
| The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side. |
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Term
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Definition
| The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side |
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Term
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Definition
| The point of concurrency of the altitudes of a triangle |
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Term
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Definition
| A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. |
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Term
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Definition
| The point of intersection of 3 or more lines |
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Term
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Definition
| A segment whose endpoints are the midpoints of two sides of a triangle |
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Term
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Definition
| A midsegment of a triangle is parallel to the third side and is half as long |
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Term
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Definition
| If one side of a triangle is longer than another side, the the angle opposite the longer side is longer than the angle opposite the shorter side. |
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Term
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Definition
| If one angle of a triangle is langer than another angle, than the side opposite the larger angle is longer than the side opposite the smaller angle. |
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Term
| Theorem 5.12 Exterior Angle Inequality |
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Definition
| The measure of an exterior angle of a triangle is greater than the measures of either of the two nonadjacent interior angles. |
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Term
| Theorem 5.13 Triangle Inequality |
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Definition
| The sum of the lengths of any two sides of a triangle is greater than the length of the third side. |
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Term
| Theorem 5.14 Hinge Theorem |
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Definition
| If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. |
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Term
| Theorem 5.15 Converse of the Hinge Theorem |
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Definition
| 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. |
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