A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular...

A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist...

Euclid. Equilateral triangle Isosceles triangle Scalene triangle Right triangle Acute triangle Obtuse triangle All types of triangles are commonly found...

^{1}} , and the triangle inequality expresses a relationship between absolute values. In Euclidean geometry, for right triangles the triangle inequality is...

the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of...

the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to...

positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle. A primitive Pythagorean...

a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. The meaning of right in right angle...

Fermat's right triangle theorem is a non-existence proof in number theory, published in 1670 among the works of Pierre de Fermat, soon after his death...

acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle...

lies inside the triangle if and only if the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an...

isosceles trapezoids, right kites, and regular polygons are cyclic, but not every polygon is. The circumcenter of a triangle can be constructed by drawing...

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...

the Pythagorean theorem, which holds only for right triangles: if ⁠ γ {\displaystyle \gamma } ⁠ is a right angle then ⁠ cos ⁡ γ = 0 {\displaystyle \cos...

quadrantal triangle can be derived from those for a right-angled triangle. The polar triangle of a polar triangle is the original triangle. If the 3 ×...

In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic...

functions output an angle of a right triangle, they can be generalized by using Euler's formula to form a right triangle in the complex plane. Algebraically...

A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is φ {\displaystyle {\sqrt {\varphi...

the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. For an equilateral triangle, all triangle centers...

composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene. The spiral is started with an isosceles right triangle, with each...

. he has proved himself mathematician." A right triangle with two equal legs is a 45-degree right triangle, all of which are similar. The length of the...

incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent...

AD) statement that Thales "was the first to inscribe in a circle a right-angle triangle". Thales was claimed to have traveled to Egypt and Babylonia, where...

adjoining right triangles, tracing a whirl of converging golden rectangles. The logarithmic spiral through the vertices of adjacent triangles has polar...

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three...

An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral...

a right isosceles triangle is a packing problem where the objective is to pack n unit circles into the smallest possible isosceles right triangle. Minimum...

side of a right triangle opposite the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called...

The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the...

Heronian triangle Pythagorean triangle Isosceles heronian triangle Primitive Heronian triangle Right triangle 30-60-90 triangle Isosceles right triangle Kepler...