Term
5.1
perpendicular bisector |
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Definition
| a bisector that is perpendicular to the segment it bisects |
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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
| 3 or more lines that intersect at a common point |
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Term
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Definition
| the point where concurrent lines intersect |
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Term
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Definition
| the point of concurrency of perpendicular bisectors |
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Term
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Definition
| the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. |
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Term
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Definition
acute: inside
right: on
obtuse: outside |
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Term
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Definition
| if a point is on the bisector of an angle, then it id 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 on the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle |
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Term
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Definition
| point of concurrency of angle bisectors |
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Term
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Definition
| the angle bisectors of a triangle intersect at a point of concurrency called the incenter that is equidistant form the sides of the triangle |
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Term
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Definition
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Term
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Definition
| segment with endpoints being a vertex of a triangle and the midpoint of the opposite side |
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Term
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Definition
point of concurrency of the medians
(always inside) |
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Term
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Definition
| the medians of a triangle intersect at a point of concurrency called the centroid that is 2/3 the distance from each vertex to the midpoint of the opposite side. |
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Term
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Definition
| segment from a vertex the makes a perpendicular angle with the opposite side |
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Term
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Definition
acute: inside
obtuse: outside
right: on one side |
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Term
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Definition
| the lines containing the altitudes of a triangle are concurrent, intersecting at a point called the orthocenter. |
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Term
5.3
definition of inequality |
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Definition
| for any real numbers a and b, a>b if and only if there is a positive number in c such that a=b+c. |
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Term
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Definition
comparison:
a is less than b, a=b, or a is greater than b
transitive:
1. if a is less than b and b is less than c, then a is less than c
2. if a is greater than b and b is greater than c, then a is greater than c
addition:
1. if agreater than b, then a+c is greater than b+c
2. if a is less than b, then a+c is less than b+c
subtraction:
1. if a is greater than b, then a-c is greater than b-c
2. if a is less than b, then a-c is less than b-c |
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Term
| exterior angle inequality |
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Definition
| the measure of an exterior angle is greater than the measure of either of its corresponding remote interior angles |
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Term
| angle side relationships in triangles 1 |
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Definition
| 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. |
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Term
| angle side relationships in triangles 2 |
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Definition
| if one angle of a triangle has a greater measure than another triangle, then the side opposite the greater angle is longer than the side opposite the lesser angle. |
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Term
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Definition
| uses a rectangular array in which you record what you have learned from clues in order to solve a logic or reasoning problem |
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Term
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Definition
| assuming conclusion false and showing that the assumption leads to a contradiction proving the conclusion true |
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Term
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Definition
| proof using indirect reasoning |
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Term
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Definition
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Term
5.5
triangle inequality theorem |
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Definition
| the sum of the lengths of any two sides of a triangle must be greater than the length of the third side |
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Term
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Definition
| if two sides of a 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 triangle, then the third side of the first triangle is larger than the third side of the second triangle |
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Term
| converse of hinge theorem |
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Definition
| if two sides of a triangle are congruent to two sides of another triangle, and the third side in the first is longer than the third side in the second triangle, then the included angle measure of the first triangle is greater than the included angle measure in the second triangle. |
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