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Recognizing special right triangles in geometry can help you to answer some questions quicker. A special right-triangle is a right triangle whose sides are in a particular ratio. You can also use the Pythagorean theorem, but if you can see that it is a special triangle it can save you some calculations.There are two types of special triangles: 45

A 45

Side 1: side 2 : hypotenuse = a : a: a√2

Find x.

This is a right triangle with two equal sides so it must be a 45

So we use, a : a: a√2

Here a = 6

Hypotenuse = a√2 = 6√2.

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Isosceles right triangle means 45

So we use, a : a: a√2

Here hypotenuse = a√2 = 10√2

Side = a = 10

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Isosceles right triangle means 45

So we use, a : a: a√2

Here hypotenuse = a√2 = 18

Side = a = 18/√2

a= (18x√2)/(√2x√2) (Rationalize the denominator)

a = 18√2/2

a = 9√2

Each side = 9√2

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