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9 terms

Centers of Triangle Part Two

Medians and Altitudes
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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
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.