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Pythagorean Theorem Explained | Learn the Basics of the Pythagorean Theorem

Discover the Pythagorean Theorem, a fundamental concept in mathematics that applies to right triangles. Explore over 200 proofs and learn how to solve for missing sides using this theorem. Find practical examples and common Pythagorean triples. Access a proof of the theorem online.

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Pythagorean Theorem Explained | Learn the Basics of the Pythagorean Theorem

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  1. Warm up 1. 3. 2.

  2. Pythagoras was a Greek philosopher and teacher He lived from 569 to 495 B. C. Often described as the “first pure mathematician” Pythagorean Theorem

  3. Pythagorean theorem – only “works” for right triangles • For right triangles, where aand b are the legs and c is the hypotenuse of the triangle. • There are more than 200 known proofs. • Check out a proof of the Theorem online at http://www.keymath.com/x19481.xml Hypotenuse (c) across from the “box” Leg (b) Leg (a)

  4. Ex1: b a • Identify your hypotenuse ( c ) • The other two sides are legs (it doesn’t matter which on you assign a or b • Plug into formula • Remember order of operations - SQUARE sides first and solve x 6 c 62 + x2 = 102 10 36 + x2 = 100 -36 -36 x2 = 64 x = 8

  5. Wall Example • How high up a wall will a 20’ ladder touch if the ladder is placed 5’ from the wall? Step 1: Identify the hypotenuse and label it “c” Ladder 20’ Step 2: Label the other two sides as “a” and “b” hypotenuse b c Step 3: Plug in and solve. 5’ a or

  6. Ex3: • Follow the steps y c a b -5 -5

  7. Classwork Solve for the missing side. Ex. 1 Ex. 2 5 y x = 3 1 Ex. 3 4 2 6 z = 5

  8. Pythagorean Triples • Any three positive integers which fit the Pythagorean equation are called Pythagorean Triples. • Common Pythagorean Triples are… 3, 4, 5 5, 12, 13 7, 24, 25

  9. Homework • Worksheet

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