Medians and Altitudes of a Triangle

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Section 5-3

• Medians and Altitudes of a Triangle

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Median

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

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Centroid of the triangle

• The point of concurrency of the three medians of
  a triangle.

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Concurrency of medians of a triangle theorem

• The medians of a triangle intersect at a point
  that is two thirds of the distance from each
  vertex to the midpoint of the opposite side.

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If P is the centroid of triangle ABC, then
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altitude

• The perpendicular segment from a vertex to the
  opposite side or to the line that contains the
  opposite side
• Every triangle has three altitudes

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Orthocenter of the triangle

• The point where the altitudes of a triangle
  intersect.

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Concurrency of altitudes of a triangle Theorem

• The lines containing the altitudes of a triangle
  are concurrent.