Perpendicular and Angle Bisectors of a 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 equidistant from all three vertices of the triangle.

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.

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

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of all three angles of the triangle. The point where they intersect is the incenter.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is the center of mass of the triangle.

Front

How do you find the centroid of a triangle?

Back

To find the centroid, locate the midpoints of each side of the triangle and draw lines from each vertex to the opposite midpoint. The intersection of these lines is the centroid.

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 90-degree angle.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

What is the relationship between the incenter and the incircle?

Back

The incenter is the center of the incircle, which is the circle that is tangent to all three sides of the triangle.