Chapter 5 Vocabulary - Relationships Within Triangles
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| altitude of a triangle | the perpendicular segment from one vertex of the triangle to the opposite side or to the line that contains the opposite side
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| centroid of a triangle | the point of concurrency of the three medians of the triangle
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| circumcenter of the triangle | the point of concurrency of the three perpendicular bisectors of the triangle
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| concurrent | three or more lines, rays, or segments that intersect in the same point
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| coordinate proof | a type of proof that involves placing geometric figures in a coordinate plane
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| equidistant | the same distance from one figure as to another figure
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| incenter of a triangle | the point of the concurrency of the three angle bisectors of the triangle
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| indirect proof | a proof in which you prove that a statement is true by first assuming that its opposite is true; if this assumption leads to an impossibility, then you have proved that the original statement is true
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| median of a triangle | a segment from one vertex of the triangle to the midpoint of the opposite side
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| midsegment of a triangle | a segment that connects the two midpoints of two sides of a triangle
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| orthocenter of a triangle | the point at which the lines containing the three altitudes of the triangle intersect
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| perpendicular bisector | a segment, ray, line, or plane that is perpendicular to a segment at its midpoint
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| point of concurrency | the point of intersection of concurrent lines, rays, or segments
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| midsegment theorem | the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side
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| perpendicular bisector theorem | if a point on the perpendicular bisector,then it is equidistant from the endpoints of the segment
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| 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
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| concurrency of a perpendicular bisectors theorem | the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
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| angle bisector theorem | 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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| converse of the angle bisector theorem | 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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| concurrency of angle bisectors of a triangle | the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
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| concurrency of a perpendicular bisectors theorem | the perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle
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| angle bisector theorem | 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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| converse of the angle bisector theorem | 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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| concurrency of angle bisectors of a triangle | the angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
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| concurrency of medians of a triangle | the medians of atriangle intersect of a triangle at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side
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| concurrency of altitude sof a triangle | the lines containing the alitiude of a triangle are concurrent
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| if one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
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| if one angle of a triangle is larger than another angle, than the side opposite the larger angle is longer than the side opposite the smalller angle
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| trianlge inequality theorem | 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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| hinge theorem | 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, than the third side of the first is longer than the third side of the second
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| converse of the hinge theorem | 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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