Difference between revisions of "Altitude"

Latest revision as of 19:15, 15 October 2023

A line segment that passes through a vertex of a triangle and is perpendicular to the line opposite to the vertex.

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-==Definition==
+<i>A line segment that passes through a vertex of a triangle and is perpendicular to the line opposite to the vertex.</i>
-In [[geometry]], an '''altitude''' of a figure is a [[cevian]] that is [[perpendicular]] to the side to which it extends.
-Usually, one is concerned with the altitude (or ''height'') of [[triangle]]s.  In particular, the altitudes of any triangle are [[concurrent]] at a point known as the [[orthocenter]].
-==Usage==
-Altitudes are mainly used to finding area of a triangle.  Furthermore, if one knows the area of a triangle and one side, the altitude to that side can be calculated.  In addition to triangles, altitudes are also useful for finding the area of quadrilaterals with at least one pair of parallel sides (rectangles, parallelograms, trapezoids).
-Because the altitude is perpendicular to a side, many right triangle tools like [[Pythagorean Theorem]] will be very useful.
 ==See also==
 *[[Geometry]]
 *[[Area]]
+*[[Orthocenter]]
 [[Category:Geometry]]
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