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

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

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...

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

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...

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...

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

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...

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

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

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...

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...

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

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

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...

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

. 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...

{Re}}\left({\text{Fourier}}\left[{\frac {\sin(x)^{5}}{x}}\right]\right)} compose the 4th row of the triangle, with alternating signs. This is a generalization...

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...

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

equilateral triangle, it will also be a rep-tile. A right triangle is a triangle containing one right angle of 90°. Two particular forms of right triangle have...

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...

circle's circumference, then |x| and |y| are the lengths of the legs of a right triangle whose hypotenuse has length 1. Thus, by the Pythagorean theorem, x and...

it. The tribar/triangle appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices...

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

The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions...

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

a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three...

triangle if and only if the triangle is acute. For a right triangle, the orthocenter coincides with the vertex at the right angle. Let A, B, C denote 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...