HW 5.3

Front

What is a median in a triangle?

Back

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

Front

If G is the centroid of triangle ABC, what is the relationship between the segments AG, GC, and GF?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment. If GF = 4, then GC = 8.

Front

What is the point of concurrency in a triangle?

Back

A point of concurrency is a point where three or more lines intersect. In a triangle, the centroid, circumcenter, incenter, and orthocenter are points of concurrency.

Front

What is the incenter of a triangle?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of a triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point of concurrency of the altitudes of a triangle.

Front

How do you find the length of a segment in a median?

Back

In a triangle, the centroid divides the median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of a triangle and is located at the intersection of the medians.

Front

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal parts.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.