Points of Concurrency in Triangles

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the 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

If G is the centroid of triangle ABC, and BE = 18, what is the length of BG?

Back

12 (The centroid divides each median into a ratio of 2:1.)

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

If AZ = 24 and X is the centroid, what is AX?

Back

16 (The centroid divides the median in a 2:1 ratio.)

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in a triangle is always 180°.

Front

What is an angle bisector?

Back

An angle bisector is a ray that divides an angle into two equal parts.

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.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.