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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