1st Points of Concurrency

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 does the centroid divide each median?

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 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 of the triangle.

Front

What does the circumcenter of a triangle represent?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle.

Front

What is the orthocenter of a triangle?

Back

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

Front

If AB = 30 and C is the centroid, what is AC if the centroid divides the median in a 2:1 ratio?

Back

AC = 20.

Front

The incenter is equidistant from which part of the triangle?

Back

The incenter is equidistant from the sides of the triangle.

Front

If AZ = 24 and X is the centroid, what is AX?

Back

AX = 16.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

What is the significance of the centroid in terms of balance?

Back

The centroid represents the center of mass, meaning it is the balance point of the triangle.