Centers of Triangles Vocab

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 segments intersect at the ORTHOCENTER of a triangle?

Back

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

Front

What is the CIRCUMCENTER of a triangle?

Back

The circumcenter is the point where the three perpendicular bisectors of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

In which type of triangle can the circumcenter be located outside the triangle?

Back

The circumcenter can be outside the triangle if the triangle is obtuse.

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 relationship between the centroid and the medians of a triangle?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

How can 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 significance of the orthocenter in a triangle?

Back

The orthocenter can provide information about the type of triangle (acute, right, or obtuse) based on its position relative to the triangle.

Front

What is the difference between the centroid and the incenter?

Back

The centroid is the intersection of the medians, while the incenter is the intersection of the angle bisectors. The centroid is the center of mass, and the incenter is the center of the inscribed circle.

Front

What is an altitude in the context of triangles?

Back

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