Special Segments of a Triangle

Front

What is a midsegment of a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

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. It represents the height of the triangle.

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 an angle bisector?

Back

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

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

If AG is a median and AG = 16, what is the length of GD?

Back

GD = 8, because the centroid divides each median into a ratio of 2:1.

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. It is equidistant from all three vertices.

Front

If point P is the circumcenter, which segment is equal to PB?

Back

PC is equal to PB, as the circumcenter is equidistant from all vertices.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is the relationship between midsegments and the sides of a triangle?

Back

A midsegment is parallel to one side of the triangle and its length is half the length of that side.