Pythagorean Theorem
Parts of a Right Triangle
Squaring the Sides
Adjust the sliders below to square each side of the triangle.
What is the area from squaring the hypotenuse of the triangle?
How are the squares of each side related to one another?
Change the lengths of the legs of the triangle below and check if the same relationship you found above still works!
What leg lengths did you test? Was the relationship you found between the squares the same as the relationship you found above?
Formalizing this Relationship
The Pythagorean Theorem
The Pythagorean theorem is named after Pythagoras of Samos (c. 570–495 BC). Pythagoras led a secretive, cult-like philosophical school in Croton, Italy, known as the Pythagoreans. Even though the name of the theorem comes from Pythagoras, the theorem was actually known to Babylonians over 1,000 years earlier.
Fun Fact: The Pythagoreans believed that numbers were the ultimate reality, essence of the universe, and possessed personalities.
Setting up the formula
Which of the following is correctly use the formula () for the given triangle?
Change the lengths of the legs of the triangle below and test if the formula is true for the triangle you create.
Determining Side Lengths
How could you determine the side lengths of the triangle above?
Solving for Hypotenuse Example
Solving for the unknown hypotenuse value.
Solve for the Leg Example
