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The Pythagorean Theorem   Evann W. Grade 8 - Ms. McClellan A Right Triangle
What is it ? <ul><li>The Pythagorean theorem is named after an ancient Grecian mathematician named Pythagoras. </li></ul><...
Using the Pythagorean Theorem <ul><li>In this following problem the object is to figure out if the triangle is a right ang...
Finding the Missing Hypotenuse <ul><li>In most problems, you must find the missing hypotenuse. In this following problem, ...
Finding the Missing Altitude/Base <ul><li>In the following problem, the base and the hypotenuse will be labeled and the al...
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The Pythagorean Theorem

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The Pythagorean Theorem

  1. 1. The Pythagorean Theorem Evann W. Grade 8 - Ms. McClellan A Right Triangle
  2. 2. What is it ? <ul><li>The Pythagorean theorem is named after an ancient Grecian mathematician named Pythagoras. </li></ul><ul><li>It is used to determine if a triangle is a right angle triangle or not and is used to figure out the length of the hypotenuse, altitude or base. </li></ul><ul><li>The theorem states that A 2 + B 2 = C 2 (altitude squared plus base squared equals the hypotenuse squared). </li></ul><ul><li>The hypotenuse is the longest side of a right angle triangle; the one opposite of the right angle. </li></ul>Altitude Hypotenuse Base A right triangle 
  3. 3. Using the Pythagorean Theorem <ul><li>In this following problem the object is to figure out if the triangle is a right angle triangle </li></ul>In this triangle, the altitude measures 6cm, the base is 8cm and the hypotenuse is 10cm. To figure out if this is a right angle triangle, keep in mind that the theorem states A 2 +B 2 =C 2 . 6cm 2 +8cm 2 =10cm 2 (you now need to find out if this is true) 6 cm 10 cm 8 cm 36 + 64 = 100 Since 6cm 2 + 8cm 2 accurately equals 10cm 2 , this shows that the triangle is a right angle triangle.
  4. 4. Finding the Missing Hypotenuse <ul><li>In most problems, you must find the missing hypotenuse. In this following problem, the base and altitude of the triangle will be labeled and the missing hypotenuse will be “C”. </li></ul>5 cm 12 cm C If the base is 12 cm and the altitude is 5 cm, what is the length of the hypotenuse? A 2 + B 2 = C2 5cm 2 + 12cm 2 = C2 25 + 144 = C 169 = C 13 = C Square the numbers  Find the square route of 169 to get the answer  (the missing hypotenuse) The missing hypotenuse is 13 cm
  5. 5. Finding the Missing Altitude/Base <ul><li>In the following problem, the base and the hypotenuse will be labeled and the altitude of the triangle will have to be found. </li></ul>A 20 cm 12 cm If the hypotenuse of the triangle is 20 cm and the base is 12 cm, what is the altitude? A 2 + B 2 = C 2 A 2 + 12cm 2 = 20 cm 2 A + 144cm = 400 cm 400 cm – 144 cm = A 256 cm = A 16 = A The missing altitude is 16cm Square the numbers  Find the square route of 256 for the answer 

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