Perpendicular Bisector
A segment, ray, line, or plane that is perpendicular to a given line or segment at a point.
Equidistant from two points
A point if its distance from each point is the same.
Distance from a point to a line
The length of the perpendicular segment from the point to the line.
Equidistant from the two lines/rays/segments
When a point is the same distance from one line as it is from another line.
Perpendicular Bisector of a Triangle
A line/ray/segment that is perpendicular to a side of the triangle at the midpoint of the side.
Concurrent lines/rays/segments
When three or more lines/rays/segments intersect in the same point.
Point of concurrency
The point of intersection of the lines/rays/segments.
Point of concurrency of an acute triangle=inside the triangle
Point of concurrency of a right triangle=on the triangle
Point of concurrency of an obtuse triangle=outside the triangle
Circumcenter of the triangle
The point of concurrency of the perpendicular bisectors of a triangle.
Angle bisector of a triangle
A bisector of an angle of the triangle.
Incenter of the triangle
The point of concurrency of the angle bisectors.
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 three medians' point of concurrency.
Altitude of a triangle
The perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side.
Orthocenter of the triangle
The point of concurrency in which the altitudes of a triangle intersect at a point.
midsegment of triangle
A line segment that connects the midpoints of two sides of a triangle
indirect proof
a proof in which you prove that a statement is true by first assuming that its opposite is true