Centers of Triangles

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 the center of mass of the triangle.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

What is the relationship between the centroid and the medians?

Back

The centroid divides each median into two segments, with the shorter segment being one third the length of the entire median.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point of concurrency of the three perpendicular bisectors of a triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

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 are perpendicular bisectors?

Back

Perpendicular bisectors are line segments that are perpendicular to a side of the triangle and bisect that side.

Front

What is the significance of the incenter?

Back

The incenter is equidistant from all sides of the triangle, making it the center of the inscribed circle (incircle).

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a, b, and c are the lengths of the sides of the triangle.

Front

What is the relationship between the angles and the incenter?

Back

The incenter divides the angles of the triangle into two equal parts.