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### 31 Cards in this Set

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 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