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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 triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.
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).
Position of some special triangles in an Euler diagram of types of triangles, using the definition that isosceles triangles have at least two equal sides, i.e. equilateral triangles are isosceles. A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas ...
The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then =, and the law of cosines reduces to = +. The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.
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]
25A0 25B0 25C0 Symbol Name Symbol Name Symbol Name Last Hex# HTML Hex HTML Hex HTML Hex Dec Picture Dec Picture Dec Picture BLACK SQUARE: BLACK PARALLELOGRAM: : BLACK LEFT-POINTING TRIANGLE
In Euclidean geometry, for right triangles the triangle inequality is a consequence of the Pythagorean theorem, and for general triangles, a consequence of the law of cosines, although it may be proved without these theorems.
In a right triangle, the altitude from each acute angle coincides with a leg and intersects the opposite side at (has its foot at) the right-angled vertex, which is the orthocenter. For acute triangles, the feet of the altitudes all fall on the triangle's sides (not extended).