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From Karnataka Open Educational Resources
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, 01:30, 6 December 2013
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| | # Is it possible to construct a triangle whose sides are 3cm, 4cm and 9cm. Give reason. | | # Is it possible to construct a triangle whose sides are 3cm, 4cm and 9cm. Give reason. |
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| − | == Centroid of a Triangle ==
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| − | From Latin: centrum -
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| − | "center", and Greek: -oid -"like" The point where
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| − | the three medians of the triangle intersect. The 'center of gravity'
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| − | of the triangle
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| − | One of a triangle's points of concurrency. Try
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| − | this Drag the orange dots at A,B or C and note where the centroid is
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| − | for various triangle shapes.
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| − | Refer to the figure . Imagine you have a
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| − | triangular metal plate, and try and balance it on a point - say a
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| − | pencil tip. Once you have found the point at which it will balance,
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| − | that is the centroid.
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| − | [[Image:KOER%20Triangles_html_m404a4c0b.gif]]
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| − | The centroid of a triangle is the point through
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| − | which all the mass of a triangular plate seems to act. Also known as
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| − | its 'center of gravity' , 'center of mass' , or barycenter.
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| − | A fascinating fact is that the centroid is the
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| − | point where the triangle's medians intersect. See medians of a
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| − | triangle for more information. In the diagram above, the medians of
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| − | the triangle are shown as dotted blue lines.
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| − | '''Centroid facts'''
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| − | * The centroid is always inside the triangle
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| − | * Each median divides the triangle into two smaller triangles of equal area.
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| − | * The centroid is exactly two-thirds the way along each median.
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| − | Put another way, the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex. These lengths are shown on the one of the medians in the figure at the top of the page so you can verify this property for yourself.
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| | == Orthocenter of a Triangle == | | == Orthocenter of a Triangle == |
