The vertex opposite the base is called the apex. The angle included by the legs is called the vertex angle and the angles that have the base as one of their sides are called the base angles. In an isosceles triangle that has exactly two equal sides, the equal sides are called legs and the third side is called the base. The same word is used, for instance, for isosceles trapezoids, trapezoids with two equal sides, and for isosceles sets, sets of points every three of which form an isosceles triangle. "Isosceles" is made from the Greek roots "isos" (equal) and "skelos" (leg). A triangle that is not isosceles (having three unequal sides) is called scalene. The difference between these two definitions is that the modern version makes equilateral triangles (with three equal sides) a special case of isosceles triangles. Terminology, classification, and examples Įuclid defined an isosceles triangle as a triangle with exactly two equal sides, but modern treatments prefer to define isosceles triangles as having at least two equal sides. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base.Įvery isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two equal sides are called the legs and the third side is called the base of the triangle. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings. The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.Įxamples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. In geometry, an isosceles triangle ( / aɪ ˈ s ɒ s ə l iː z/) is a triangle that has two sides of equal length. Therefore, the perimeter of the triangle is 12.Isosceles triangle with vertical axis of symmetry In this case you would add 3 + 4 + 5 and get 12. ![]() Finally, add all of the side lengths together to find the perimeter. Therefore, the length of the unknown side is 5. ![]() Then, you would take the square root of 25 to find c, which is 5. For example, if the length of the known sides are 3 and 4, you would just add 3^2+ 4^2, or 9 + 16, and get 25. Just use the Pythagorean theorem, which is a^2+ b^2 = c^2, where a and b are the lengths of the known sides and c is the length of the unknown hypotenuse. If you only know the length of 2 of the triangle’s sides, you can still find the perimeter if it’s a right triangle, which means the triangle has one 90-degree angle. Therefore, the perimeter of the triangle is 15. For example, if the length of each side of the triangle is 5, you would just add 5 + 5 + 5 and get 15. To find the perimeter of a triangle, use the formula perimeter = a + b + c, where a, b, and c are the lengths of the sides of the triangle.
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