Pythagorean Theorem.pptx
- 2. Define the Pythagorean Theorem 1 Define a right triangle 2 Identify real-life applications 4 Apply the Pythagorean Theorem 3 LEARNING TARGETS
- 3. The Pythagorean Theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. INTRODUCTION
- 4. HISTORY The ancient Greek mathematician and philosopher Pythagoras is credited with discovering this relationship in the 6th century BCE due to the prominence of his religious-mathematical school in Croton, Italy. That said, It was likely independently discovered in several different cultures. There is evidence of its use in Egypt, Babylon, and China as far back as the 20th century BCE.
- 5. The Pythagorean Theorem has been proved through hundred of methods and new proofs are still being discovered. Here is an example of a visual proof showing the squares of the sides. Notice, 9 + 16 = 25! VISUAL PROOFS 9 16 25
- 6. UNDERSTANDING RIGHT TRIANGLES A right triangle is any triangle with one right angle. The two sides that form the right angle are called the legs. The side opposite the right angle is called the hypotenuse. A right angle creates many special relationships between the sides and angles of the triangle and is the basis of the mathematical branch of trigonometry.
- 7. Determine which side you are trying to find. Identify the two legs of the triangle and the hypotenuse. Note their lengths. Substitute your lengths into the Pythagorean Theorem equation and solve for the missing value. 1 2 3 USING THE PYTHAGOREAN THEOREM
- 8. leg hypotenuse USING THE PYTHAGOREAN THEOREM 1 Identify the two legs of the triangle and the hypotenuse. Note their lengths.
- 9. 8 in 15 in ? USING THE PYTHAGOREAN THEOREM Determine which side you are trying to find. 2
- 10. 2 a = 8 in b = 15 in USING THE PYTHAGOREAN THEOREM Substitute your lengths into the Pythagorean Theorem equation and solve for the missing value. c = ? 8 + 15 = c 2 2 2 64 + 225 = c2 289 = c 2 17 = c 3
- 11. Building and architecture 1 Navigation and GPS 2 Games and sports 3 REAL LIFE APPLICATIONS
- 12. The Pythagorean Theorem describes the relationship between the sides of a right triangle. SUMMARY It can be used to find the missing side of a right triangle, which can be applied to solve many real-life problems. Understanding the Pythagorean Theorem is a great foundation for learning trigonometry, the distance formula, and more!
- 13. What other examples can you think of for using the Pythagorean Theorem in your life?