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A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
As a consequence of the Pythagorean theorem, the hypotenuse is the longest side of any right triangle; that is, the hypotenuse is longer than either of the triangle's legs. For example, given the length of the legs a = 5 and b = 12, then the sum of the legs squared is (5 × 5) + (12 × 12) = 169, the square of the hypotenuse.
A similar proof uses four copies of a right triangle with sides a, b and c, arranged inside a square with side c as in the top half of the diagram. [6] The triangles are similar with area 1 2 a b {\displaystyle {\tfrac {1}{2}}ab} , while the small square has side b − a and area ( b − a ) 2 .
The three sides of the triangle are named as follows: [1] The opposite side is the side opposite to the angle of interest; in this case, it is . The hypotenuse is the side opposite the right angle; in this case, it is . The hypotenuse is always the longest side of a right-angled triangle. The adjacent side is the remaining side; in this case ...
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]
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