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In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of those two segments equals the altitude.
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle (1 ⁄ 4 turn or 90 degrees).
The process of drawing the altitude from a vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection . Altitudes can be used in the computation of the area of a triangle : one-half of the product of an altitude's length and its base's length (symbol b ) equals the triangle's area: A = h b /2.
The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments the hypotenuse is split into.
The geometric mean has from time to time been used to calculate financial indices (the averaging is over the components of the index). For example, in the past the FT 30 index used a geometric mean. [8] It is also used in the CPI calculation [9] and recently introduced "RPIJ" measure of inflation in the United Kingdom and in the European Union.
Right triangle altitude: Image title: The altitude of a right triangle from its right angle to its hypotenuse is the geometric mean of the lengths of the segments into which the hypotenuse is split, as drawn by CMG Lee. Width: 100%: Height: 100%
Two triangles are said to be similar, if every angle of one triangle has the same measure as the corresponding angle in the other triangle. The corresponding sides of similar triangles have lengths that are in the same proportion, and this property is also sufficient to establish similarity.
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);