M3 6.1 Centers of 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 all three vertices of the triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the altitudes of a triangle intersect. It can be located inside, outside, or on the triangle depending on the type of triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the medians of a triangle intersect. It is the center of mass and divides each median into a 2:1 ratio.

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 does the Hinge Theorem state?

Back

The Hinge Theorem states that if two triangles have two sides equal and the included angle of one triangle is larger than the included angle of the other, then the third side of the first triangle is longer than the third side of the second triangle.

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

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, draw the altitudes from each vertex to the opposite side. The point where all three altitudes intersect is the orthocenter.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, draw the angle bisectors of each angle of the triangle. The point where they intersect is the incenter.