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Dual polygon. Kite. In Euclidean geometry, an isosceles trapezoid (isosceles trapezium in British English) is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of equal measure, [1 ...
In geometry, an isosceles triangle (/ aɪ ˈ s ɒ s ə l iː z /) is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
The midsegment of a trapezoid is one of the two bimedians (the other bimedian divides the trapezoid into equal areas). The height (or altitude) is the perpendicular distance between the bases. In the case that the two bases have different lengths (a ≠ b), the height of a trapezoid h can be determined by the length of its four sides using the ...
Any square, rectangle, isosceles trapezoid, or antiparallelogram is cyclic. A kite is cyclic if and only if it has two right angles – a right kite.A bicentric quadrilateral is a cyclic quadrilateral that is also tangential and an ex-bicentric quadrilateral is a cyclic quadrilateral that is also ex-tangential.
In calculus, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) [a] is a technique for numerical integration, i.e., approximating the definite integral: (). The trapezoidal rule works by approximating the region under the graph of the function f ( x ) {\displaystyle f(x)} as a trapezoid and calculating its area.
The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...
An orthodiagonal quadrilateral (yellow). According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals ...
Interior angle Δθ = θ 1 −θ 2. The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of cosines, which states that where is the angle between sides and . [45] When is radians or 90°, then , and the formula reduces to the usual Pythagorean theorem.
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