Euclidean triangle can have more than one obtuse angle. Acute and obtuse triangles are the two different types of oblique triangles—triangles that are...

isosceles triangles represented the working class, with acute isosceles triangles higher in the hierarchy than right or obtuse isosceles triangles. As well...

developed later, and sine and cosine per se first appeared centuries afterward in India. The cases of obtuse triangles and acute triangles (corresponding...

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

Acute and obtuse triangles (oblique triangles) Spiral of Theodorus Trirectangular spherical triangle Di Domenico, Angelo S., "A property of triangles...

theorem) For acute triangles, the feet of the altitudes all fall on the triangle's sides (not extended). In an obtuse triangle (one with an obtuse angle),...

between the Fermat point and X13 the domain of triangles with an angle exceeding 2π/3 is important; in other words, triangles for which any of the following...

Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of...

diagonal to form a pair of obtuse Robinson triangles; in contrast to the P2 tiling, these are larger than the acute triangles. The matching rules distinguish...

angle, then the two triangles are congruent. If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side...

+ b2 < c2, then the triangle is obtuse. Edsger W. Dijkstra has stated this proposition about acute, right, and obtuse triangles in this language: sgn(α...

orthocenter is in an acute triangle's interior, on the right-angled vertex of a right triangle, and exterior to an obtuse triangle. In the complex plane...

two golden gnomons and a central golden triangle. The five points of a regular pentagram are golden triangles, as are the ten triangles formed by connecting...

or union (in the case of acute or obtuse angles, respectively). It corresponds to a circular sector of infinite radius and a flat pencil of half-lines...

solution for every polygon and for every convex set, two special cases that both apply to triangles. Every acute triangle has three inscribed squares...

opposite angle being obtuse, drawing a line at a negative angle means going outside the triangle.) In coastal navigation, a triangle's circumcircle is sometimes...

the geometric shape. Triangle Acute and obtuse triangles Altitude (triangle) Area bisector of a triangle Angle bisector of a triangle Angle bisector theorem...

called Heronian triangles or rational triangles; in this article, these more general triangles will be called rational Heronian triangles. Every (integral)...

considered the three cases right, obtuse, and acute that the summit angles of a Saccheri quadrilateral can take and after proving a number of theorems...

trapezoid Triangle Acute and obtuse triangles Equilateral triangle Euler's line Heron's formula Integer triangle Heronian triangle Isosceles triangle List...

geometry, triangle inequalities are inequalities involving the parameters of triangles, that hold for every triangle, or for every triangle meeting certain...

between integer triangles and rational triangles. Sometimes other definitions of the term rational triangle are used: Carmichael (1914) and Dickson (1920)...

triangles can also be seen as a trigonal trapezohedron when its coplanar triangles are merged into rhombi. The two golden rhombohedra are the acute and...

to as the obtuse and acute Robinson triangles. A golden triangle and two golden gnomons tile a regular pentagon. These isosceles triangles can be used...

the areas of the two triangles formed by the other diagonal. The areas S and T of some two opposite triangles of the four triangles formed by the diagonals...

fifth postulate, otherwise, they must be either acute or obtuse. He showed that the acute and obtuse cases led to contradictions using his postulate,...

The obtuse golden triangle is the gnomon of acute golden triangle The acute golden triangle is the gnomon of the obtuse golden triangle The acute golden...

theorem) but one with acute triangle faces and with edges that in general do not lie along the edges of the given obtuse triangles. Two more types of tetrahedron...

For instance, propositions twelve and thirteen of book two of the Elements are the laws of cosines for obtuse and acute angles, respectively. Theorems on...

nonobtuse triangle mesh is a polygon mesh composed of a set of triangles in which no angle is obtuse, i.e. greater than 90°. If each (triangle) face angle...