math
7th Grade - Pythagorean theorem

7th Grade lesson

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.
hypothenuse

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.
right-angled triangle

In other words :
Pythatgoras theorem

Or :
Pythagorean theorem


Examples of the use of the theorem :


Calculate SX.
calculating Pythagorean theorem
calculating Pythagorean theorem><br />
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calculating Pythagorean theorem
calculating Pythagorean theorem
calculating Pythagorean theoremcm
Pythagorean theorem
Calculate AD.
application of Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theoremcm
Pythagorean theorem
Calculate NU.
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theorem
Pythagorean theoremcm

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.

reciprocal of Pythagorean theorem
To show that the triangle ABC is right-angled, we calculate separately reciprocal calculation of Pythagorean theorem and calculs réciproque du theorème de pythagore.

reciprocal calculations of Pythagorean theorem
reciprocal calculations of Pythagorean theorem, so
reciprocal calculations of Pythagorean theorem, 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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