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31 Cards in this Set
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 Back
Perpendicular Bisector

A segment, ray, line, or plane that is perpendicular to a segment at its midpoint


Equidistant from Two Points

The same distance from one line as from another point


Perpendicular Bisector 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


Distance from a Point to a Line

The length of the perpendicular segment from the point to a line


Equidistant from the Two Lines

The same distance from one line as from another line


Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle


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


Perpendicular Bisector of a Triangle

A line, ray, or segment that is perpendicular to a side of a triangle at the midpoint of the side


Concurrent Lines

Three or more lines that intersect in the same point


Point of Concurrency

The point of intersection of concurrent lines


Circumcenter of the Triangle

The point of concurrency of the perpendicular bisectors of a triangle


Concurrency of Perpendicular Bisectors of a Triangle

The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle


Angle Bisector of a Triangle

A bisector of a an angle of the triangle


Incenter of the Triangle

The point of concurrency of the angle bisectors of a triangle


Concurrency of Angle Bisector of a Triangle

The angle bisectorsof a triangle intersect at a point that is equidistant from the sides of the triangle


Median of a Triangle

A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side


Centroid of the Triangle

The point of concurrency of the medians of a triangle


Concurrency of Medians of a Triangle

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


Altitude of a Triangle

The perpendicular segment from a vertex of a triangle to the opposite side or to the line that contains the opposite side


Orthocenter of the Triangle

The point of concurrency of the lines containing the altitudes of a triangle


Concurrency of Altitudes of a Triangle

The lines containing the altitudes of a triangle are concurrent


Midsegment of a Triangle

A segment that connects the midpoints of two sides of a triangle


Midesegment Theorem

The segment connecting the midpoints of two sides of a triangle is parrallel to the third side and is half as long


Theorem 5.10

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


Theorem 5.11

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle


Exterior Angle Inequality

The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles


Triangle Inequality

The sum of the lengths of any two sides of a triangle is greater than the length of the third side


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


Hinge Theorem

If two side 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 then the third side


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 second, then the included angle of the second
