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5-3 Medians and Altitudes of a Triangle

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- Use the properties of Medians of a triangle
- Use the properties of Altitude of a triangle

- 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.

- 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

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

- 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: