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How to use the Pythagorean theorem?

right triangles

Pythagorean theorem is one of the most used theorems in right angle triangles. It gives us precise relation between length of sides. The right triangle is a triangle that has right angle.

It says that:

a^2 + b^2 = c^2

Where c is always length of hypotenuse. That means that point C will always be a vertex of a right triangle.
What does this theorem actually say?

It says that in a right triangle, the sum of areas of squares whose sides are the same length as legs of a right triangle is equal to the area of square whose side is the same length as the hypotenuse.

pythagorean theorem

Image credit: Wikimedia Commons user AmericanXplorer13

The right Triangle whose length of sides is equal to 3, 4 and 5 is called the Egyptian triangle.

Let’s forget that we know that the length of hypotenuse is equal to 5 and try to calculate it using Pythagorean theorem.

We have:

egyptian triangle

\ c^2 = a^2 + b^2

Where a = 4, and b = 3.

c^2 = 4^2 + 3^2
c^2 = 16 + 9
c^2 = 25

If we know lengths of any two sides of a right triangle, we can use this theorem to quickly find third.

egyptian triangle task

c^2 = a^2 + b^2

Where c = 10, and b = 83.

a^2 = c^2 - b^2
a^2 = 100 - 64
a^2 = 36
a = 6


Pythagorean theorem worksheets

Right triangle

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  Radicals (467.3 KiB, 229 hits)

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  Special right triangles (389.8 KiB, 265 hits)

  Multi-step triangle problems (175.1 KiB, 229 hits)