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Lesson 7

Lesson 7. Pythagorean Theorem. What is the Pythagorean Theorem. In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side, and the two shorter sides that form the right angle are called legs. Hypotenuse c. a Leg. b Leg. So what is it then?.

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Lesson 7

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  1. Lesson 7 Pythagorean Theorem

  2. What is the Pythagorean Theorem • In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side, and the two shorter sides that form the right angle are called legs. Hypotenuse c a Leg b Leg

  3. So what is it then? • The Pythagorean theorem relates the lengths of the legs to the length of the hypotenuse. • “In any right triangle, the square of hypotenuse is equal to the sum of the squares of the lengths of the legs. “ • In math terms, that means: c2= a2+b2

  4. Let’s try one • In Triangle RST, what is the length of side RS? • Use the formula. What are we looking for? • Substitute in what we know: 252=a2+242 • 625=a2 + 576 • 49=a2 • A=7 R 25m S 24m T

  5. Next example • Tanya’s TV screen is shaped like a rectangle that is 20 inches long and 15 inches wide. The size of a TV screen is measured by the length of its diagonal. What is the size of Tanya’s TV screen?

  6. Time for practice • What is the length of the missing side? • A rectangular park has a length of 40 meters and a width of 30 meters. How long will a diagonal path from one corner of the park to the other measure? 45 cm 27 cm x

  7. Last but not least • The solid lines below show the route that Shawn usually takes when he drives from his house to the public library. The dashed line shows a shortcut that Shawn recently discovered. • If Shawn takes the shortcut, how many kilometers does he drive? Show your work. • How many fewer kilometers does Shawn drive if he takes the shortcut than if he takes his regular route?

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