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.

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5-3 Medians and Altitudes of a Triangle

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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

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

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

Interesting Property of a Centroid

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


Definitions1

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.


5 3 medians and altitudes of a triangle

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


5 3 medians and altitudes of a triangle

Remember the Distance and Midpoint formulas:

Write them below:

Distance Formula:

Midpoint Formula:


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