5-3 Triangle Centers

5-3 Triangle Centers - The orthocenter is formed by the...

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Triangle Centers Section 5-3

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Unlike squares and circles, triangles have many centers. The ancient Greeks found four: incenter, centroid, circumcenter, and orthocenter.
Centroid The centroid is formed by the intersection of the medians of a triangle. The centroid is the center of gravity. 2x x

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Centroid Theorem (5-8) The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median. 2x x
Circumcenter The circumcenter is the center of the circumcircle and is formed by the intersection of the perpendicular bisectors of the sides of a triangle. P A B PC PB PA = =

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Circumcenter Theorem (5-6) The circumcenter is equidistant from the 3 vertices. P A B C PC PB PA = =
Orthocenter

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Unformatted text preview: The orthocenter is formed by the intersection of the 3 altitudes. Theorem 5-9 The lines that contain the altitudes of a triangle are concurrent. Euler Line The Euler line is the line on which the orthocenter, centroid, and circumcenter lie. Incenter The incenter is the center of the inscribed circle and is formed by the intersection of the angle bisectors Incenter Theorem (5-7) The incenter of a triangle is equidistant from each side of the triangle. Joke Time What be a pirate afraid of? The Daaaaarrrrrrrrrrrrk! What be a pirate’s favorite class? Arrrrrrrrrrrrrrrrrrrrt How much does it cost for a pirate to pierce his ears? A bucaneer!...
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This note was uploaded on 12/01/2011 for the course MATH 105 taught by Professor Towns during the Fall '10 term at BYU.

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5-3 Triangle Centers - The orthocenter is formed by the...

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