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Median definition

A segment that connects a vertex of a triangle to the midpoint of the opposite side. Only makes congruent segments. Doesn't have to be perpendicular. *Always passes through the vertices of a triangle.

Centroid

Point of concurrency of the medians of a triangle.

Location of Centroid

Always inside triangle.

Length of Centroid

Vertex to centroid is 2/3's of median. Centroid to midpoint of side is 1/3.

Altitude definition

A segment from a vertex of a triangle perpendicular to the line containing the opposite side. Doesn't have to cut side in half. *Always passes through vertices of a triangle

Orthocenter

point of concurrency of the altitudes of a triangle

Location of orthocenter

Acute triangle=inside

Right triangle=on

Obtuse triangle=outside

Right triangle=on

Obtuse triangle=outside

Euler's Line

Circumcenter, orthocenter, and centroid are always in a line in a triangle.

Equilateral triangle

A triangle with congruent sides.

The circumcenter, orthocenter, incenter, and centroid are in the same location.

The circumcenter, orthocenter, incenter, and centroid are in the same location.