Pythagorean Theorem

The Pythagorean Theorem

*Created by Greek Philosopher, Pythagoras, to  find the longest side of a right triangle .

​1. Statement
The Pythagorean Theorem states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.

*The longest side of a right triangle is called
the hypotenuse.

​​1.Determining Distance

​​2.Construction and Architecture:

​​3.Navigation

​ 2. Application of The Pythagorean Theorem

​*If a square is made on each side of a right triangle, the sum of the area of two smaller squares will be equal to the area of the square on the longer side

a²+b²=c²
​
^{Area of small square} a^{2
Area of medium square}b^{2
Area of large square} c²

​*A set of whole numbers that makes the relationship true is called a Pythagorean triple.
For example, {3, 4, and 5} is a Pythagorean triple because 32 + 42 = 52 .

​3. Pythagorean Triple

*If you know the lengths of any two sides of a right triangle (two legs, or one leg and the hypotenuse), you can use the Pythagorean theorem to find the length of the third side.

​4. Applying the Pythagorean Theorem

Textbook page no 124

Try Questions....

Multiple Choice

which one is hypotenuse?

• XY

• XZ

• YZ

• b

Multiple Choice

• A ladder is leaning against a wall. The foot of the ladder is 6 meters away from the wall, and the ladder reaches 8 meters up the wall. How long is the ladder?

• D) 16 meters
• B) 11 meters
• C) 13 meters
• A) 10 meters