Geometry Worksheets to Practice Using the Pythagorean Theorem

Pythagorean theorem

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The Pythagorean Theorem is believed to have been was discovered on a Babylonian tablet circa 1900-1600 B.C.

The Pythagorean Theorem relates to the three sides of a right triangle. It states that c2=a2+b2, C is the side that is opposite the right angle which is referred to as the hypotenuse. A and b are the sides that are adjacent to the right angle.

The theorem simply stated is: the sum of the areas of two small squares equals the area of the large one.

You will find that the Pythagorean Theorem is used on any formula that will square a number. It's used to determine the shortest path when crossing through a park or recreation center or field. The theorem can be used by painters or construction workers, think about the angle of the ladder against a tall building for instance. There are many word problems in the classic math textbooks that require the use of the Pythagorean Theorem.

History Behind Pythagorean's Theorem

Illustration of Pythagorean Theorem

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Hippasus of Metapontum was born in the 5th Century BC. It is believed that he proved the existence of irrational numbers at a time when the Pythagorean belief was that whole numbers and their ratios could describe anything that was geometric. Not only that, they didn't believe there was a need for any other numbers.

The Pythagoreans were a strict society and all discoveries that happened had to be directly credited to them, not the individual responsible for the discovery. The Pythagoreans were very secretive and did not want their discoveries to 'get out' so to speak. They considered whole numbers to be their rulers and that all quantities could be explained by whole numbers and their ratios. An event would happen that would change the very core of their beliefs. Along came Pythagorean Hippasus who discovered that the diagonal of a square whose side was one unit could not be expressed as a whole number or a ratio.

What Is the Hypotenuse?

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Simply put, the hypotenuse of a right triangle is the side opposite the right angle. It is sometimes referred to by students as the long side of the triangle. The other two sides are referred to as the legs of the triangle. The theorem states that the square of the hypotenuse is the sum of the squares of the legs. 

The hypotenuse is the side of the triangle where C is. Always understand that the Pythagorean Theorem relates the areas of squares on the sides of the right triangle

Worksheet #1

Pythagorean worksheet

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Worksheet #2

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Worksheet #3

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Worksheet #6

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Worksheet #7

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Worksheet #8

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Worksheet #9

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Worksheet #10

Pythagorean worksheet

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