Інтегрований урок з математики та англійської мови. Тема: «Теорема Піфагора та її застосування»

THE PYTHAGOREAN THEOREM

Define the Pythagorean Theorem1 Define a right triangle2 Identify real-life applications4 Apply the Pythagorean Theorem3 LEARNING TARGETS

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

HISTORYThe 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.

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 PROOFS91625

UNDERSTANDING RIGHT TRIANGLEShypotenuselegleg. 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.

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. 123 USING THE PYTHAGOREAN THEOREM

leghypotenuseleg. USING THE PYTHAGOREAN THEOREM1 Identify the two legs of the triangle and the hypotenuse. Note their lengths.

8 in15 in?USING THE PYTHAGOREAN THEOREMDetermine which side you are trying to find. 2

2a = 8 inb = 15 in. USING THE PYTHAGOREAN THEOREMSubstitute your lengths into the Pythagorean Theorem equation and solve for the missing value. c = ?8 + 15 = c 22264 + 225 = c 2289 = c 217 = c 3

Building and architecture1 Navigation and GPS2 Games and sports3 REAL LIFE APPLICATIONS

The Pythagorean Theorem describes the relationship between the sides of a right triangle. SUMMARYIt 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!

What other examples can you think of for using the Pythagorean Theorem in your life?