5-4%20Medians%20and%20Altitudes

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5-4 Medians and Altitudes
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Median of a Triangle

• A segment whose endpoints are a vertex and the
  midpoint of the opposite side.

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• A triangles three medians are always concurrent,
  and are always concurrent on the interior of the
  triangle.

In a triangle, the point of concurrency of the
medians is the centroid of the triangle. The
point is also called the center of gravity of a
triangle because it is the point where a
triangular shape will balance.
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Altitude of a triangle

• The perpendicular segment from a vertex of the
  triangle to the line containing the opposite
  side.
• An altitude of a triangle can be inside the
  triangle or outside, or in right triangles it is
  a side of the triangle.

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• The lines that contain the altitudes of a
  triangle are concurrent at the orthocenter of the
  triangle. The orthocenter of a triangle can be
  inside, on(for right triangles the orthocenter
  will be the vertex at the right angle), or
  outside the triangle.

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Orthocenter with coordinate geometry

• Need to use a system of equations

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Circumcenter with coordinate geometry

• Need to use a system of equations

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Centroid with coordinate geometry

• Average of xs and ys