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Pythagorean theorem

Lecture



Theorem.

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

  Pythagorean theorem

Evidence.

Let Δ ABC be rectangular and ∠ ABC be straight.
Let us draw the height BD from the vertex B of the right angle. By definition cosine of an angle

  Pythagorean theorem

Add the resulting equality by term:

  Pythagorean theorem

The theorem is proved.
created: 2014-10-05
updated: 2021-03-13
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Planometry

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