Medians%20and%20Altitudes%20of%20Triangles

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Section 5.3

• Medians and Altitudes of Triangles

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Definitions

• Median A median is a line from a vertex of a
  triangle to the midpoint of the opposite side of
  the triangle.
• Altitude An altitude is a line from a vertex of
  a triangle that is perpendicular to the line
  containing the opposite side.

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Centroid

• The medians of a triangle are concurrent at a
  point called the centroid.
• The centroid is two-thirds the distance from the
  vertex to the midpoint of the opposite side.

Centroid Diagram
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Orthocenter

• The altitudes of a triangle are concurrent at a
  point called the orthocenter.
• Some interesting facts about the orthocenter
• The orthocenter, centroid, and circumcenter are
  collinear. The line is called the Euler line.
• Theorem - Take a triangle with vertices at A, B
  and C, and let H be its orthocenter. The
  orthocenter for any of the triangles formed from
  three of these four points is the fourth point.

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Example
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Homework

• Pg 282 8-12, 17-23, 45