Centers of Triangles

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 of the triangle.

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 the center of the circumcircle, which passes through all three vertices.

Front

What is the Centroid of a triangle?

Back

The Centroid is the point where the medians of a triangle intersect. It divides each median into a ratio of 2:1.

Front

What is the Orthocenter of a triangle?

Back

The Orthocenter is the point where the altitudes of a triangle intersect. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

If AC = 16, what is AM if M is the midpoint of AC?

Back

AM = 8 (since M is the midpoint, it divides AC into two equal segments).

Front

What is a Median in a triangle?

Back

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

Front

What is an Angle Bisector?

Back

An Angle Bisector is a line that divides an angle into two equal parts.

Front

What is a Perpendicular Bisector?

Back

A Perpendicular Bisector is a line that divides a segment into two equal parts at a right angle.

Front

What is an Altitude in a triangle?

Back

An Altitude is a perpendicular segment from a vertex to the line containing the opposite side.

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. The point where they intersect is the Circumcenter.