Chapter 5 Geometry (McDougal Littell)

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