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

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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