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**Special Shortcuts for 45-45-90 and 30-60-90 Triangles**

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Triangle If you know the length of the leg, multiply that by 2 to find the length of the hypotenuse.

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Triangle If you know the length of the hypotenuse and you want the length of the leg, divide the length of the hypotenuse by 2.

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Triangle When working with a triangle, you will have three different lengths: Short leg Long leg Hypotenuse

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**30-60-90 Triangle If you know the length of the short leg:**

The length of the hypotenuse is twice the length of the short leg. The length of the long leg is the length of the short leg multiplied by 3.

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**30-60-90 Triangle If you know the length of the hypotenuse:**

Find the length of the short leg by dividing the length of the hypotenuse by 2. Now that you know the length of the short leg, multiply it by 3 to find the length of the long leg.

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**30-60-90 Triangle If you know the length of the long leg:**

Find the length of the short leg by dividing the length of the long leg by 3. Now that you know the length of the short leg, multiply it by 2 to find the length of the hypotenuse.

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The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

The Pythagorean Theorem x z y. For this proof we must draw ANY right Triangle: Label the Legs “a” and “b” and the hypotenuse “c” a b c.

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