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2.24 Pythagorean Theorem

Pythagorean Theorem:
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras.

The Pythagorean Theorem states that: The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.

In other words:
In a right angled triangle the square of the hypotenuse is equal to sum of the square of the other two sides.
If a, b and c are three sides of a right angled triangle and c is the hypotenuse, then: .

Proof: Lets consider a right angle triangle with a = 3 and b = 4 and hypotenuse, c = 5
Draw 3 squares on each side of the triangle.
Then the areas of the two squares will be equal to the area of the square on the hypotenuse.

Area of the square on the side a = 3 cm is 3x3 = 9 sq cms.
Area of the square on the side b = 4 cm is 4x4 = 16 sq cms.
Area of the square on the side c = 3 cm is 5x5 = 25 sq cms.
Therefore area of the square on c = area of square on the side a + area of square on the side b.


If a = 5 cm and b = 12 cm then c2 = a2 + b2
c = 13

Directions: On a sheet of paper state and prove the pythagorean theorem and write at least 5 examples of your own.