Triangle Segments and Centers

Front

What is the centroid of a triangle?

Back

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

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of the sides of the triangle intersect. It is equidistant from all three vertices.

Front

Where is the circumcenter located in an acute triangle?

Back

The circumcenter is located inside the triangle.

Front

Where is the circumcenter located in a right triangle?

Back

The circumcenter is located at the midpoint of the hypotenuse.

Front

Where is the circumcenter located in an obtuse triangle?

Back

The circumcenter is located outside the triangle.

Front

What is the incenter of a triangle?

Back

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

Front

What is an angle bisector?

Back

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

Front

What is the relationship between the incenter and the triangle's sides?

Back

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

Front

What is the orthocenter of a triangle?

Back

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

Front

What is the relationship between the orthocenter and the triangle's vertices in an acute triangle?

Back

In an acute triangle, the orthocenter is located inside the triangle.