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...

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

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...

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...

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...

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...

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...

. 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...

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...

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...

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

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...

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...

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...

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...

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...

definitions of the sine and cosine functions in terms of the sides of a right triangle are: sin ⁡ θ = o p p o s i t e h y p o t e n u s e = b c {\displaystyle...

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...