Centers of Triangles

Front

What is the definition of an angle bisector in a triangle?

Back

An angle bisector is a line segment that divides an angle into two equal angles.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the circle inscribed within the triangle.

Front

What is a median in a triangle?

Back

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

Front

What are altitudes in a triangle?

Back

Altitudes are line segments from a vertex of a triangle perpendicular to the line containing the opposite side.

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, and it is the center of the circumcircle.

Front

How many angle bisectors does a triangle have?

Back

A triangle has three angle bisectors, one for each angle.

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.

Front

What is the centroid of a triangle?

Back

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

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the orthocenter of a triangle?

Back

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