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Pythagorean Theorem
Be silent, or say something

Pythagoras was a philosopher and religious leader from Samos, an island off of Greece, (between around 570–495 B.C.E.). He became well-known for his developments in mathematics, astronomy, and music theory. A secret group, the Pythagoreans, was formed in the city of Croton where Pythagoras taught a curricula of four mathemata or studies consisting of arithmetica (number theory), geometria (geometry), astrologia (astronomy), and harmonia (music). From this secret brotherhood, which believed, "Brotherhood is the greatest purification," we have learned about the Pythagorean Theorem (although it is highly probable and likely that the theorem has been around for much longer. The Pythagoreans, however, provided the first logical proof of the theorem.

The Basics in the Pythagorean

right triangle: triangle where two legs form an angle that ameasures 90º

the right angle is indicated by a little square connecting the legs that form the 90º angle


legs: the three sides that make up the right triangle

Each leg is labeled with a letter: a, b, and c. The letters a and b and used for the two legs that make up the right angle and the letter c is used to denote the hypotenuse (the leg opposite the right angle).


legs a and b: are the two shorter legs that make up the right angle (90º)


hypotenuse: the side OPPOSITE the right angle (90º angle) is called the hypotenuse and is the LONGEST side; it is labeled c

*the hippo is to remind you of the hypotenuse

Okay, now for the

The theorem, as denoted by the Pythagoreans, is quite simple:

The important thing is you have to know what to DO with the letters and the numbers when posed with a problem! Yep, that's right! And, guess what…if you understand some of the basics (hint, hint!), then it really is as easy as it appears! So, let's get started so that you can see what I am talking about!

Short Legs =

Lots of problems give you the two shorter legs but NOT the hippo, er, the hypotenuse. If that's the case, then this is the flow map (equation) you should use to find your answer!

a and b are short legs and the hypotenuse is the big hippo (longest leg)
One Big Hippo

Sometimes, a right triangle problem provides information on the hypotenuse and one leg. This is like a hippo with a broken leg! You need to find the measure of the missing or broken leg so use the subtraction equation as shown here.

Big Hippo Breaks a Leg

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