6.1-6.3, Points of Concurrency

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

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 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. Its position varies depending on the type of triangle (acute, right, or obtuse).

Front

What are angle bisectors?

Back

Angle bisectors are segments that divide an angle into two equal parts. They are used to find the incenter of a triangle.

Front

What are perpendicular bisectors?

Back

Perpendicular bisectors are segments that cut a side of a triangle into two equal parts at a right angle. They are used to find the circumcenter.

Front

What are medians in a triangle?

Back

Medians are segments that connect a vertex of a triangle to the midpoint of the opposite side. They are used to find the centroid.

Front

What are altitudes in a triangle?

Back

Altitudes are segments that extend from a vertex of a triangle perpendicular to the opposite side. They are used to find the orthocenter.

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

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of at least two angles of the triangle. The point where they intersect is the incenter.