5-4%20Medians%20and%20Altitudes - PowerPoint PPT Presentation

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

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A triangle s 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 ... – PowerPoint PPT presentation

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


1
5-4 Medians and Altitudes
2
Median of a Triangle
  • A segment whose endpoints are a vertex and the
    midpoint of the opposite side.

3
  • 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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10
  • 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.

11
Orthocenter with coordinate geometry
  • Need to use a system of equations

12
Circumcenter with coordinate geometry
  • Need to use a system of equations

13
Centroid with coordinate geometry
  • Average of xs and ys
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