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The Pythagorean Theorem

He is one of the most popular polygons in existence, mainly because of his problem-solving abilities. A right triangle has one angle equal to 90 degrees. A right triangle can also be an isosceles triangle--which means that it has two sides that are equal. A right isosceles triangle has a degree angle and two degree angles. This is the only right triangle that is an isosceles triangle.

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This version of the right triangle is so popular that plastic models of them are manufactured and used by architects, engineers, carpenters, and graphic artists in their design and construction work. Another interesting right triangle is the degree triangle. The ratio of this triangle's longest side to its shortest side is "two to one.

Pythagorean Theorem -- from Wolfram MathWorld

It too is manufactured in plastic and widely used in design, drawing, and building applications. You can find an endless number of examples of right triangles.

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One of the most famous is the "3, 4, 5 triangle. The Egyptians used this triangle for land surveying.

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Some believe that they also used it to help design their pyramids. Whether they did or not, the triangle is still used by surveyors.

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Carpenters and woodworkers also use it to make their corners square. Pythagoras was a Greek mathematician who lived about years ago, and who developed the most famous formula in geometry, possibly in all of mathematics!

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He proved that, for a right triangle, the sum of the squares of the two sides that join at a right angle equals the square of the third side. The third side--the side opposite the right angle--is called the hypotenuse of the right triangle. The two shorter sides are usually called "legs. This formula is called the Pythagorean Theorem in honor of Pythagoras. Description for the calculation of right triangles and the Pythagorean theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Pythagorean theorem 3 - Right triangles and trigonometry - Geometry - Khan Academy

The hypotenuse is the longest side of a right triangle. It is always across from the right angle.

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A Pythagorean triplet is made up of three natural numbers, which may appear as lengths of the sides of a right triangle. A Pythagorean triple is a right triangle whose sides are in the ratio The side lengths do not need to measure 3, 4, and 5; however, they do need to reduce to that ratio. For example, the side lengths 9, 12, and 15 are a Pythagorean triple because it simplifies to the ratio