Centers of Triangles

Front

What is the definition of a perpendicular bisector in a triangle?

Back

A perpendicular bisector is a line segment that divides another segment into two equal parts at a 90-degree angle.

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.

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.

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 the orthocenter of a triangle?

Back

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

Front

What are altitudes in a triangle?

Back

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

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex to the midpoint of the opposite side.

Front

What are angle bisectors in a triangle?

Back

Angle bisectors are segments that divide an angle into two equal angles.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection is the circumcenter.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of all three angles; their intersection is the incenter.