7th Grade - Pythagorean theorem

# 9 - Pythagorean theorem

Pythagoras is the name of a scholar who lived more than 2000 years ago in Greece and who discovered a mathematical properties that enables us to calculate lengths in a right-angled triangle.

A right-angled triangle is a triangle which has a right-angle. If we know the length of two edges of a right-angled triangle, we can find out the length of the third edge. We need to use Pythagorean theorem.

## Hypotenuse of a triangle

In a right-angled triangle, the largest edge is called the hypotenuse.

## Pythagorean theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the two other edges.
 In other words : Or :

Examples of the use of the theorem :

 Calculate SX. cm Calculate AD. cm Calculate NU. cm

In an problem, if you are asked to show that a triangle is a right-angled triangle and you know the length of the three edges, then you must use the reciprocal of Pythagorean theorem.

## Reciprocal of Pythagorean theorem

If in a triangle, the length of the largest edge is equal to the sum of the squares of the two other edge, then this triangle is a right-angled triangle.

To show that the triangle ABC is right-angled, we calculate separately and .

, so
, therefore, according to the reciprocal of Pythagorean theorem, the triangle ABC is right-angled at B.

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Pythagorean theorem

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