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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).
In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. [1] Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13). A primitive Pythagorean triple is one in which a, b and c are coprime (the greatest common divisor of a ...
The name is derived from the Pythagorean theorem, stating that every right triangle has side lengths satisfying the formula + =; thus, Pythagorean triples describe the three integer side lengths of a right triangle. However, right triangles with non-integer sides do not form Pythagorean triples.
Set square shaped as 45° - 45° - 90° triangle The side lengths of a 45° - 45° - 90° triangle 45° - 45° - 90° right triangle of hypotenuse length 1.. In plane geometry, dividing a square along its diagonal results in two isosceles right triangles, each with one right angle (90°, π / 2 radians) and two other congruent angles each measuring half of a right angle (45°, or ...
A right triangle with the hypotenuse c. In a right triangle, the hypotenuse is the side that is opposite the right angle, while the other two sides are called the catheti or legs. [7] The length of the hypotenuse can be calculated using the square root function implied by the Pythagorean theorem.
A triangle's shape is uniquely determined by the lengths of the sides, so its metrical properties, including area, can be described in terms of those lengths. By Heron's formula, = () where = (+ +) is the semiperimeter, or half of the triangle's perimeter. Three other equivalent ways of writing Heron's formula are
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
One of the triangle area formulas involving the semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem) pairs of opposite sides have lengths summing to the semiperimeter—namely, the area is the product of the inradius and the semiperimeter: