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5-3 Medians and Altitudes of a Triangle

5-3 Medians and Altitudes of a Triangle. Use the properties of Medians of a triangle Use the properties of Altitude of a triangle. Definitions. A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side.

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5-3 Medians and Altitudes of a Triangle

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  1. 5-3 Medians and Altitudes of a Triangle • Use the properties of Medians of a triangle • Use the properties of Altitude of a triangle

  2. Definitions • A median of a triangle is a segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. • The point of concurrency point is called the Centroid. • The centroidis always inside the triangle.

  3. Special Property of Centroid: • 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

  4. Interesting Property of a Centroid • The centroid is the balancing point of a triangular model of uniform thickness and density.

  5. Definitions • An Altitude of a triangle is the perpendicular segment from a vertex to the opposite side or the line than contains the opposite side (height of the triangle). • The orthocenter is the point of concurrency of the altitudes.

  6. An Altitude and its orthocentercan lie inside, on, or outside the triangle.

  7. Remember the Distance and Midpoint formulas: Write them below: Distance Formula: Midpoint Formula:

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