Triangle Centers Review

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point that is equidistant from the vertices of a triangle.

Front

If G is the centroid of triangle ABC and GE = 7, what is the length of BE?

Back

The length of BE is 21.

Front

In a triangle, if ZX = 3 and X is the centroid, what is the length of AZ?

Back

The length of AZ is 9.

Front

Which point in a triangle is equidistant from the sides?

Back

The incenter.

Front

What are the three medians of a triangle?

Back

The three medians are line segments that connect each vertex of the triangle to the midpoint of the opposite side.

Front

What is the centroid of a triangle?

Back

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

Front

How is the circumcenter constructed in a triangle?

Back

The circumcenter is constructed by finding the intersection of the perpendicular bisectors of the sides of the triangle.

Front

What is the relationship between the centroid and the vertices of a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all sides of the triangle.

Front

What is the significance of the orthocenter in a triangle?

Back

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