Centroid and Orthocenter
Median of a triangle: the median of a triangle is a segment from a vertex to the midpoint of the opposite side. (This segment is not necessarily perpendicular.)
Centroid: The point of concurrency of the three medians.
Altitude of a triangle: An altitude of a triangle is the perpendicular segment from a vertex to the opposite side or to the line that contains the opposite side. ( It is not a bisector.)
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Orthocenter: The point at which the lines containing the three altitudes of a triangle intersect is called the orthocenter of the triangle.
The medians of a triangle K
ex. 1:
intersect at a point that is 2/3 of the distance from each vertex to the midpoint of the opposite side.
M
J
L
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Find KM
Find KE
B
ex. 2:
Find GE
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G
A
C
Find BE
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ex. 3: Find the orthocenter of the triangle.
Remember : the orthocenter of a triangle is the concurrency of the altitudes drawn from each angle to the opposite side.
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