Pythagorean Theorem Definition Pythagorean Theorem Definition In geometrical mathematics, a polygon can be defined as a geometrical shape or figure that is enclosed with straight lines. In a simple mean we can define the polygon as a closed figure that are made up of several lines segment that are interlinked to each other. In the shape of polygon the interlinked sides neither are nor intersect to each other. In the mathematical definition we can say that a polygon is popularly known as plane figure which is enclosed by closed path. In the shape of polygon different straight lines are interconnected to each other, these sides are popularly known as edges of the polygon. The word polygon come from Greek word ‘polusgonia’, which is formed by two words ‘polus’ and ‘gonia’. Here the word polus refers to the many and the word gonia refers to the angle. The polygon can be considered as a basic shape of the geometry that is formed on two dimensional plane. Know More About Arc of a Circle Math.Tutorvista.com
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If the length of the other two sides ‘a’ and ‘b’ are known then ‘c’ could be calculated as, c = √ (a2 + b2), If the length of the opposite side to the right angle that is hypotenuse is ‘c’ and one of the other two sides either a or ‘b’ are known then the length of the other leg can be calculated with either of the following equations, a = √ (c2 – b2), Or for the side ‘b’ b = √ (c2 – a2), The Pythagorean equation shows the relation between sides of a triangle, thus if the lengths of any two sides of a triangle are known then the length of the third side could be determined easily. In any right angle triangle the hypotenuse (that is the side that is opposite to the right angle) here we are taking it ‘c’, is greater than any one of the sides of the triangle but its less than the sum of the sides of that triangle. The formation of this theorem is basically the law of cosines that allows the determination of the length of the third side of the triangle and the length of the other two sides are given. The Pythagoras theorem can be explained with the help of four copies of a right triangle that have the sides x, y and z or it may be a, b and c. These triangles are arranged in a square of the side ‘l’. The area of a square could be presented in two different ways as, As the sum of the area of the two rectangles and squares, Learn More Perpendicular Lines Definition Math.Tutorvista.com
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(a + b)2 = a2 + b2 + 2ab, As the sum of the areas of a square and the four triangles, (a + b)2 = c2 + 4(ab / 2) = c2 + 2ab, On putting the two right hand side equations equal, a2 + b2 + 2ab = c2 + 2ab, => a2 + b2 = c2. The converse of the Pythagoras theorem is also true according to which if a triangle satisfies Pythagoras theorem than that triangle would be a right angle triangle.
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In geometrical mathematics, a polygon can be defined as a geometrical shape or figure that is enclosed with straight lines. In a simple mean...