5-3 Medians and Altitudes of a Triangle - PowerPoint PPT Presentation

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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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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.

• The point of concurrency point is called the Centroid.

• The centroidis always inside the triangle.

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

Interesting Property of a Centroid

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

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.

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

Remember the Distance and Midpoint formulas:

Write them below:

Distance Formula:

Midpoint Formula: