Triangle Centers Review

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 balancing point of the triangle.

Front

How do you find the centroid of a triangle with vertices at (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

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.

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 intersection point 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.

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 intersection point is the incenter.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position varies depending on the type of triangle.

Front

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, draw the altitudes from each vertex to the opposite side. The intersection point of these altitudes is the orthocenter.

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 segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is the significance of the circumcenter in a triangle?

Back

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