1. Special Segments in Triangles
Geometry
Unit 5, Lessons 5 & 6

2. Perpendicular Bisectors in a Triangle
A perpendicular bisector of a side of a triangle is a line (or portion of a line) that passes through the midpoint of the side and is perpendicular to that side.
The three perpendicular bisectors of a triangle intersect at the circumcenter.
The circumcenter can be INSIDE, OUTSIDE or ON the triangle.
The circumcenter is equidistant from each of the vertices of the triangle.

3. Angle Bisectors of a Triangle
An angle bisector of a triangle is a line (or portion of a line) containing a vertex of the triangle and bisecting that angle.
The three angle bisectors of a triangle intersect at the incenter.
The incenter is equidistant from each side of the triangle.

4. Medians of a Triangle
A median of a triangle is a line (or portion of a line) containing a vertex of the triangle and the midpoint of the opposite side.
The three medians of a triangle intersect at the centroid.
The centroid is the point of balance for any triangle.
The centroid divides each median into two segments so that the shorter one is ½ the length of the longer one.

5. Altitudes of a Triangle
An altitude of a triangle is a line (or portion of a line) containing a vertex of the triangle and is perpendicular to the opposite side (or line containing that side).
The three altitudes of a triangle intersect at the orthocenter.
The orthocenter can be INSIDE, OUTSIDE or ON the triangle.

6. Midsegments of a Triangle
A midsegment of a triangle is a segment with endpoints that are the midpoints of two sides of the triangle.
A midsegment of a triangle is parallel to one side of the triangle.
A midsegment is ½ the length of its corresponding side.
The midsegments divide a triangle into four congruent triangles.