Bisectors, Medians, and Altitudes Lesson 5.1

Perpendicular Bisector – line, segment, or ray that passes through the midpoint of the segment and forms a right angle with it. Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment.

Angle Bisector – line, segment, or ray that divides an angle into two congruent parts. Any point on the angle bisector is equidistant from the sides of the angle. Any point equidistant from the sides of an angle lies on the angle bisector.

In Triangles Perpendicular Bisector – goes thru the midpoint of a side and forms a right angle with the side. - may or may not go thru vertex - three in each triangle -may meet inside, outside, or on triangle -meeting point (point of concurrency) is called circumcenter -circumcenter is equidistant to vertices of triangle.

In Triangles 2. Angle Bisector – divides angle into two congruent parts. - three in each triangle -meet inside the triangle -meeting point (point of concurrency) is called the incenter. -incenter is equidistant to sides of triangle.

In Triangles Median – segment from the vertex to the midpoint of the opposite side. - three in each triangle -meet inside the triangle -meeting point (point of concurrency) is called the centroid. -centroid is two thirds the distance from a vertex to the

In Triangles altitude – segment from the vertex perpendicular to the opposite side. May be inside, on, our outside triangle. - three in each triangle -meet inside, on, or outside the triangle -meeting point (point of concurrency) is called the orthocenter.