Centers of Triangles

Front

What is the centroid of a triangle?

Back

The centroid is the point where all three medians of a triangle intersect.

Front

What segments intersect at the centroid?

Back

Medians.

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.

Front

How many medians does a triangle have?

Back

A triangle has three medians.

Front

What is the relationship between the centroid and the medians?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is the significance of the circumcenter?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it the center of the circumcircle.

Front

What is the significance of the orthocenter?

Back

The orthocenter is the point where the altitudes of the triangle meet, and its position varies depending on the type of triangle.

Front

What is the significance of the incenter?

Back

The incenter is equidistant from all three sides of the triangle, making it the center of the incircle.