Difference between revisions of "Median of a triangle"
m (Triangle median moved to Median of a triangle: sounds better) |
m (LaTeXed numbers) |
||
(6 intermediate revisions by 4 users not shown) | |||
Line 1: | Line 1: | ||
− | A median of a [[triangle]] is a [[cevian]] of | + | 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 == | == See Also == | ||
− | *[[ | + | * [[Altitude]] |
− | *[[Angle bisector]] | + | * [[Angle bisector]] |
− | *[[Perpendicular 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
This article is a stub. Help us out by expanding it.