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

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.

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.

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.

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.

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.