Centers of Triangles

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

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. It is equidistant from all three vertices of the triangle.

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

What is the Centroid of a triangle?

Back

The Centroid is the point where the medians of a triangle intersect. It is the center of mass and divides each median into a 2:1 ratio.

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 a perpendicular bisector in a triangle?

Back

A perpendicular bisector is a line that divides a side of the triangle into two equal parts at a right angle.

Front

What is an angle bisector in a triangle?

Back

An angle bisector is a line that divides an angle of the triangle into two equal angles.

Front

How many centers can be found in a triangle?

Back

There are four main centers in a triangle: Incenter, Circumcenter, Orthocenter, and Centroid.

Front

What is the relationship between the Incenter and the sides of a triangle?

Back

The Incenter is equidistant from all three sides of the triangle.