Pythagorean TheoremBy Mrs. Muller

Why the Pythagorean Theorem

You can solve for a missing side of a right triangle.

You can tell if something is a right triangle.

You can make sure an angle is 90 degrees.

What is the formula

a2+b2=c2

The a and b represent the legs of the right triangle (it does not matter which one is which)

The C represents the hypotenuse and has to be where the hypotenuse is.

The hypotenuse is a cross from the 90 degree angle and is the longest side.

Solving For a Missing Side(Hypotenuse Side)

First label the sides of the triangles with the a, b, and c

Then take the equation a2+b2=c2

and substitute the values that are next to the given sides: b=4, a=3, and c=c

32+42=c2, then use PEMDAS to simplify the equation before solving.

9+16=c2, 25=c2, then solve for the variable 25 = c2 Square root both sides; c=5

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Solving For a Missing Side(A Leg Side)

First label the sides of the triangle with a, b, and c

Then take the equation a2+b2=c2

and substitute the values that are next to the given sides: a= 6, b=b, c=10

62+b2=102, then use PEMDAS to simplify the equation before solving.

36+b2=100, then solve for the variable 36+b2-36=100-36, b2+0=64, b2 = 64 , b=8

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To tell if it is a Right Triangle When given the values: a=9, b=12, c=15, just

substitute the values given for each variable into the equation.

a2+b2=c2

92+122=152 (substitute the values in)81+144=225225=225 (Simplify by following PEMDAS)

Since they are equal to each other at the end it is a right triangle, and that also means that one of the angles is 90 degrees

If the equation proves false in the end then that means that it is not a right triangle and none of the angles can be 90 degrees.