Difference between revisions of "Median of a triangle"
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− | + | A '''median''' of a [[triangle]] is a [[cevian]] of the triangle that joins one [[vertex]] to the [[midpoint]] of the opposite side. | |
− | + | In the following figure, <math>AM</math> is a median of triangle <math>ABC</math>. | |
− | + | <center>[[Image:median.PNG]]</center> | |
+ | Each triangle has <math>3</math> medians. The medians are [[concurrent]] at the [[centroid]]. The [[centroid]] divides the medians (segments) in a <math>2:1</math> ratio. | ||
− | * [[ | + | [[Stewart's Theorem]] applied to the case <math>m=n</math>, gives the length of the median to side <math>BC</math> equal to <center><math>\frac 12 \sqrt{2AB^2+2AC^2-BC^2}</math></center> This formula is particularly useful when <math>\angle CAB</math> is right, as by the Pythagorean Theorem we find that <math>BM=AM=CM</math>. |
+ | |||
+ | == See Also == | ||
+ | * [[Altitude]] | ||
+ | * [[Angle bisector]] | ||
+ | * [[Mass points]] | ||
+ | * [[Perpendicular bisector]] | ||
+ | {{stub}} | ||
+ | [[Category:Definition]] |
Revision as of 14:58, 4 April 2020
A median of a triangle is a cevian of the triangle that joins one vertex to the midpoint of the opposite side.
In the following figure, is a median of triangle .
Each triangle has medians. The medians are concurrent at the centroid. The centroid divides the medians (segments) in a ratio.
Stewart's Theorem applied to the case , gives the length of the median to side equal to
This formula is particularly useful when is right, as by the Pythagorean Theorem we find that .
See Also
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