Altitudes, Medians, & Centers

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

How do you find the centroid of a triangle given its vertices?

Back

To find the centroid (G) of a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3), use the formula: G = ( (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3 ).

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

Front

What is an altitude in a triangle?

Back

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

Front

Where do the altitudes of a triangle intersect?

Back

The altitudes of a triangle intersect at a point called the orthocenter.

Front

What is the orthocenter of a triangle?

Back

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

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, and it is the center of the circumcircle.

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 the center of the incircle.

Front

How many medians can a triangle have?

Back

A triangle has exactly three medians, one from each vertex.