Special Segments in Triangles

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 the vertices of the triangle.

Front

What is an angle bisector?

Back

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

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.

Front

What is a median in a triangle?

Back

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

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.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

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 a triangle?

Back

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

Front

What is the orthocenter of a triangle?

Back

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

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is a perpendicular segment from a vertex to the opposite side.