M3 6.1 Centers of Triangles

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the three 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 three perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle, which passes through all three vertices.

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the three 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 three medians of a triangle intersect. It is also known as the center of mass or balance point of the triangle.

Front

What are angle bisectors in a triangle?

Back

Angle bisectors are segments that divide an angle into two equal parts. Each triangle has three angle bisectors, one for each angle.

Front

What are perpendicular bisectors in a triangle?

Back

Perpendicular bisectors are segments that cut a side of the triangle into two equal parts at a right angle. Each triangle has three perpendicular bisectors, one for each side.

Front

What are medians in a triangle?

Back

Medians are segments that connect a vertex of the triangle to the midpoint of the opposite side. Each triangle has three medians.

Front

What are altitudes in a triangle?

Back

Altitudes are segments that extend from a vertex of the triangle perpendicular to the opposite side. Each triangle has three altitudes.

Front

How do you find the Incenter of a triangle?

Back

To find the Incenter, construct the angle bisectors of each angle in the triangle. The point where they all intersect is the Incenter.

Front

How do you find the Circumcenter of a triangle?

Back

To find the Circumcenter, construct the perpendicular bisectors of each side of the triangle. The point where they all intersect is the Circumcenter.