Medians and Altitudes of Triangles

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect.

Front

What segments intersect at the centroid of a triangle?

Back

The centroid is the point of concurrency of the three medians of a triangle.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the relationship between the centroid and the lengths of the segments it creates?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

If G is the centroid and GF = 4, what is the length of GC?

Back

GC = 8, because the centroid divides the median in a 2:1 ratio.

Front

What is the perpendicular bisector of a segment?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

If BE = 15, what is EG if E is the midpoint of segment BG?

Back

EG = 5, because BE is twice the length of EG.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the altitudes of a triangle intersect.