Pythagorean Theorem

Right Triangle Fun! 1. Get out a piece of paper. 2. Get out a pencil or pen. 3. Get out a calculator. Read each slide. Answer the questions The Pythagorean Theorem can be used to find the length of the missing side of a right triangle if you know the lengthof the other two sides. 5 12 X What kind of triangles does the Pythagorean Theorem work on? *** You can click the back button << to see the previous slide if you want to! Acute Triangles Right Triangles Obtuse Triangles Any kind of triangle The formula for the Pythagorean Theorem is: leg^{2} + leg^{2} = hypotenuse^{2}5 12 X What in the world are Legs or Hypotenuse? Legs always make a right angle! They Hypotenuse must be the longest! L E G H Y P LEG O T E N U S E L E G H Y P LEG O T E N Which side must be the longest? U S E leg hypotenuse It doesn't matter which way the triangle is facing. The legs always make the right angle and the side opposite the right angle is always the hypotenuse. hypotenuse leg leg z Which side is the hypotenuse? (click on the correct answer) x x y y z z If you picked , you were correct!!!yx x y y z Which side is the hypotenuse? (click on the correct answer) x z y x z y Did you pick the right answer? x z x y None of these, it's not a right triangle! Which side is the hypotenuse? (click on the correct answer) x z y x z y Just because it looks like a right triangle, doesn't mean it is. It has to be marked or labeled or some way let you know there is a right angle! Did you catch my trickery? z x y So how do we use this Pythagorean Theorem to find the missing side of a right triangle? Well, we've covered the first step already. First we have to identify the legs and the hypotenuse. The legs have lengths 3 and 4 and we don't know how long the hypotenuse is. x 4 3 Once we've identified the legs and hypotenuse, we substitute these for the letters in the formula. leg^{2} + leg^{2} = hyp^{2}(3) ^{2} + (4)^{2} = (x)^{2} x 4 3 So the hypotenuse is 5! Simplify and Solve First the exponents (3) ^{2} + (4)^{2} = (x)^{2}9 + 16 = x ^{2}25 = x ^{2} √25 =√x ^{2}5 = x Write this equation on your paper and solve. Make sure you show all your work! 5 ^{2} + x^{2} = 13^{2}Type your answer below! x = Did you get the right answer? Here's my work: 5 ^{2} + x^{2} = 13^{2}25 + x^{2} -25= 169 -25 x ^{2} = 144x =√144 x = 12 Which side is the hypotenuse? x 40 41 They're all hypotenuses! There isn't a hypotenuse! x 40 41 Formula: leg^{2} + leg^{2} = hyp^{2}So the missing leg has a length of 9! 41 was the correct answer!x x ^{2} + 40^{2} = 41^{2}x ^{2} + 1600 -1600= 1681-1600x ^{2} = 81x = 9 40 41 Now you try one: Which way should you set up the equation? (Pick one) (8) ^{2} + (6)^{2} = (n)^{2}6 8 n (6) ^{2} + (n)^{2} = (8)^{2}If you picked: (8) ^{2} + (6)^{2} = (n)^{2}YOU'RE CORRECT!!!You could also write: (6) ^{2} + (8)^{2} = (n)^{2}Write down the equation on your paper. (6) ^{2} + (8)^{2} = (n)^{2 }Which one of these show up in your work? Now solve your equation. 28 = n ^{2} 100 = n ^{2} 196 = n ^{2}How long is the hypotenuse (c)? PICK ONE100 50 10 100 = n ^{2}is CORRECT!!! √10 = √n ^{2}10 = n The hypontenuse is 10 units long. (15) ^{2} + (17)^{2} = (x)^{2}Now you try one: Which equation is correct? (Pick one)15 17 (15) ^{2} + (x)^{2} = (17)^{2}x Which equation shows up in your work? If you picked: (15) ^{2} + (x)^{2} = (17)^{2}YOU'RE CORRECT!!!You could also write: (x) ^{2} + (15)^{2} = (17)^{2} x ^{2} = 2^{2} x ^{2} = 35^{2}_{}x ^{2} = 64x = 8 which means the leg is 8 units long! x ^{2} = 64 is CORRECT!So, which answer is correct? 15 17 x = 8 which means the hypotenuse is 8 units long! x x = 8 which meansthe leg is 8 units longis the correct answer!15 17 x Let's try one more: Which way should you substitute the numbers? (Pick one)(13) ^{2} + (5)^{2} = (m)^{2}13 5 m (m) ^{2} + (5)^{2} = (13)^{2}Which is the correct simplification of the equation? (PICK ONE)If you picked: (m) ^{2} + (5)^{2} = (13)^{2}YOU'RE CORRECT!!!You could also write: (5) ^{2} + (m)^{2} = (13)^{2} m ^{2} + 25 = 169 m ^{2} + 10 = 26What is the next step and the result? PICK ONE Subtract 25. m ^{2} = 144 Take the square root of both sides. m + 5 = 13 m ^{2} + 25 = 169 is CORRECT!!!13 5 m You must subtract 25. m ^{2} = 144 m =72 units m =12 units m =144 units √m ^{2} = √144m = 12 The leg is 12 units long. Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 80^{2} = 64^{2}x ^{2} + 64^{2} = 80^{2}64 ^{2} + 80^{2} = x^{2}64 80 x Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 64^{2} = 80^{2}80 64 48 80 x Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 144^{2} = 17^{2}x ^{2} + 17^{2} = 144^{2}17 ^{2} + 144^{2} = x^{2}x 17 144 Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 45^{2} = 36^{2}x ^{2} + 36^{2} = 45^{2}36 ^{2} + 45^{2} = x^{2}36 45 x Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 60^{2} = 11^{2}x ^{2} + 11^{2} = 60^{2}11 ^{2} + 60^{2} = x^{2}60 x 11 The first equation should be x ^{2} +25^{2} =24^{2}It's not a right triangle, so you can't use the Pythagorean Theorem The x ^{2} =49 is wrong.I Have no idea x ^{2} +24^{2} =25^{2}x ^{2} +576=625x ^{2} =49x = 7 Why is this problem WRONG? 24 25 x Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 16^{2} = 34^{2}x ^{2} + 34^{2} = 16^{2}16 ^{2} + 34^{2} = x^{2}x 34 16 Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 22.5^{2} = 14^{2}x ^{2} + 14^{2} = 22.5^{2}14 ^{2} + 22.5^{2} = x^{2}22.5 x 14 The first equation should be 6 ^{2} +10^{2} =x^{2}It's not a right triangle, so you can't use the Pythagorean Theorem The 10 ^{2} - 6^{2} isn't 4^{2}.I Have no idea x ^{2} +6^{2} =10^{2}x ^{2} =10^{2 -}6^{2}x ^{2} =4^{2}x = 16 Why is this problem WRONG? x 90 10 6 The first equation should be 3 ^{2} +x^{2} =4^{2}It's not a right triangle, so you can't use the Pythagorean Theorem The x ^{2} =25 is wrong.I Have no idea 3 ^{2} +4^{2} =x^{2}25 =x ^{2}5 =x Why is this problem WRONG? 4 25 x 3 70 Which equation is correct? What letter or number is on the hypotenuse? What's the final answer for x? x ^{2} + 20.8^{2} = 56.08^{2}x ^{2} + 56.08^{2} = 20.8^{2}20.8 ^{2} + 56.08^{2} = x^{2}20.8 56.08 x 35 The next set of problems have a Right Triangle in them somewhere, so you'll have to find the triangle to solve it! 45 What Kind of Triangle is this? Acute Triangle Right Triangle Obtuse Triangle Not enough info Now do another quiz from your list! THE END |

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