Centroid and Centers of Triangles Flashcard

Front

If AC = 16, what is AM?

Back

AM = 8 (Since the centroid divides the median in a 2:1 ratio)

Front

The altitudes of a triangle intersect at the _________________________.

Back

Orthocenter

Front

The circumcenter is equidistant from each ______________ of the triangle.

Back

vertices

Front

If LB = 4, what is CL?

Back

CL = 4 (The centroid divides the median in a 2:1 ratio)

Front

The centroid cuts each median into two segments. The shorter segment is ___________ the length of the entire segment.

Back

one third

Front

What is the definition of a centroid in a triangle?

Back

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

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians.

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 longer segment being twice the length of the shorter segment.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect.