5.3 Centroids and Vocabulary

Front

What is the point of concurrency where the angle bisectors of a triangle meet?

Back

Incenter

Front

In triangle JKL, if P is the incenter, what is the distance from P to the sides of the triangle?

Back

The incenter is equidistant from the sides of the triangle.

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.

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 type of lines are the altitudes of a triangle?

Back

Altitudes are perpendicular segments from a vertex to the line containing the opposite side.

Front

What is the definition of a median in a triangle?

Back

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

Front

How do you find the length of a segment using the Pythagorean theorem?

Back

If a triangle has legs of lengths a and b, and hypotenuse c, then a² + b² = c².

Front

What is the definition of a centroid in a triangle?

Back

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

Front

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

Back

The centroid divides each median into two segments, one of which is twice the length of the other.

Front

What is the definition of the circumradius?

Back

The circumradius is the radius of the circumcircle, the circle that passes through all vertices of the triangle.