6.2 - 6. 3 Homework Bisectors, Medians and Altitudes of aTriangl

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 coordinates of the centroid of a triangle with vertices A(x1, y1), B(x2, y2), C(x3, y3)?

Back

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

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

What is the point of concurrency of the medians called?

Back

The point of concurrency of the medians is called the centroid.

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 triangle's incircle.

Front

How do you find the length of a segment from the centroid to a vertex?

Back

The length from the centroid to a vertex is two-thirds the length of the median from that vertex to the midpoint of the opposite side.

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 orthocenter of a triangle?

Back

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

Front

If G is the centroid and GF = 4, what is the length of GC?

Back

GC = 8, because GC is twice the length of GF.

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.