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# Math 5.1 - 5.6

### Math vocab for 5.1 - 5.6

angle bisector theorem If a point is on a bisector of an angle, then it is equidistant from the two sides of the angle
angle bisector theorem converse If a point is in the interior of an angle and is equidistant from the sides of an angle, then it lies on the bisector of the angle
equidistant the same distance
perpendicular bisector a segment, ray, line, or plane that is perpendicular to a segment at its midpoint
perpendicular bisector theorem if a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment
perpendicular bisector theorem converse if a point is equidistant from the endpoints of a segment then it is on the perpendicular bisector of the segment
angle bisector of a triangle a bisector of an angle of the triangle
circumcenter of the triangle the point of concurrency of the perpendicular bisectors of a triangle
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
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
concurrent lines three or more lines that intersect in the same point
incenter of the triangle the point of concurrency of the angle bisectors of a triangle
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
point of concurrency the point of intersection of concurrent lines
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
centroid of the triangle the point of concurrency of the medians of a triangle always inside the triangle
concurrency of altitudes of a triangle the lines containing the altitudes of a triangle are concurrent there is always an orthocenter
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
median of a triangle a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side
orthocenter of a triangle the point of concurrency of the lines containing the altitudes of a triangle
midsegment of a triangle a segment that connects the midpoints of two sides of a triangle
midsegment theorem the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long
exterior angle inequality theorem the measure of an exterior angle of a triangle greater than the measure of either of the two nonadjacent interior angles
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
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
triangle inequality theorem the sum of the lengths of any two sides of a triangle is greater than the length of the third side
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 then the third side of the first is longer than the third side of the second
hinge theorem converse if two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longe rthan the third side of the second then the included angle of the first is larger than the included angle of the second
Created by: jumpthemoon