5.1-5.2. Special Segments in triangles

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 altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the point of concurrency of the medians called?

Back

The point of concurrency of the medians is called the centroid.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all 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, and it is equidistant from all vertices.

Front

What is the orthocenter of a triangle?

Back

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

Front

How do you find the centroid of a triangle?

Back

The centroid can be found by averaging the coordinates of the vertices of the triangle.

Front

What is the relationship between the centroid and the medians?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

What is the significance of the incenter in triangle construction?

Back

The incenter is the center of the inscribed circle (incircle) of the triangle, which touches all three sides.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.