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a a2 + b2 = c2 To apply the theorem, you will need to use your knowledge of squares & square roots. The Pythagorean Theorem is one of the most familiar theorems in mathematics. b c Click "OK" leg "The sum of the squares of the legs in a right triangle is equal to the square of it's hypotenuse." leg hypotenuse Lets test your knowledge of squares & square roots. 42= 72= 122= 152= 252= Type in your answers √81= √25= √100= √121= √64= Look over the example and then try some on your own. √a2 = √36 a2 = 36 a = 6 Inverse operations must be used when solving for a missing side of a right triangle. The inverse operation for squaring a value is square rooting. example: Notice how the square & the square root cancelled each other out. Type in your answers b2 = 4 b = try outs: c2 = 400 c = Now that we have reviewed the skills needed to apply the Pythagorean Theorem, let's get down business. Look at the given triangle below. See if you can identify & label the triangle correctly. "a" for the short leg. "b" for the other leg. "c" for the hypptenuse. Type in your answers. a If you labeled your triangle like below, then you were correct. b "a" for the short leg. "b" for the other leg. "c" for the hypptenuse. c Click "OK" b a c -9 -9 32+b2 = 52 a2+b2 = c2 9 +b2 = 25 Now that you can correctly label a right triangle, let's get started with finding a missing side. √b2=√16 b2= 16 b=4 c=5 b=? Set up the equation Simplify Solve using inverse operations a=3 Type in your answers a=9 2+ 2 = 2 a2+ b2 = c2 + b2 = b=? b2 = c=15 b = Finding the missing side. Solve using inverse operations Simplify Set up the equation 2+ 2 = 2 a2 + = a2+ b2 = c2 Type in your answers a2 = a = c=10 b=8 a=? Finding the missing side. Simplify Solve using inverse operations Set up the equation 2+ 2 = 2 + = c2 a2+ b2 = c2 Type in your answers c = = c2 = c c=? b=16 a=12 Finding the missing side. Simplify Solve using inverse operations Set up the equation 2+ 2 = 2 + = c2 a2+ b2 = c2 Type in your answers c = = c2 = c c=? b=24 a=18 Cynthia drove 56 miles due south and 90 miles due west. If she drove in a straight line back to the point where she started, how far will she drive? 146 You are now ready for the final question! 106 Choose the best answer ? miles 90 miles 70 56 miles 11236 |