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area of grey square = area of grey rectangle: = = 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.
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 ...
A triangle with sides <, semiperimeter = (+ +), area, altitude opposite the longest side, circumradius, inradius, exradii,, tangent to ,, respectively, and medians,, is a right triangle if and only if any one of the statements in the following six categories is true. Each of them is thus also a property of any right triangle.
Altitude is a vertical measurement between a reference datum and an object. ... The exact definition and reference datum varies according to the context (e.g ...
The area of a triangle is half the area of any parallelogram on the same base and having the same altitude. The area of a rectangle is equal to the product of two adjacent sides. The area of a square is equal to the product of two of its sides (follows from 3).
Points J, K, L are the midpoints of the line segments between each altitude's vertex intersection (points A, B, C) and the triangle's orthocenter (point S). For an acute triangle , six of the points (the midpoints and altitude feet) lie on the triangle itself; for an obtuse triangle two of the altitudes have feet outside the triangle, but these ...
One acre equals 1 ⁄ 640 (0.0015625) square mile, 4,840 square yards, 43,560 square feet, [2] or about 4,047 square metres (0.4047 hectares) (see below).While all modern variants of the acre contain 4,840 square yards, there are alternative definitions of a yard, so the exact size of an acre depends upon the particular yard on which it is based.
The altitude from A intersects the extended base at D (a point outside the triangle). In a triangle, any arbitrary side can be considered the base. The two endpoints of the base are called base vertices and the corresponding angles are called base angles. The third vertex opposite the base is called the apex.