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Geometry 5.7

Geometry 5.7. The Pythagorean Theorem. Learning Targets. Students will be able to… Use the Pythagorean theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles. Warm-up. Homework Check. Homework Check. Vocabulary. c. a. b. Right Triangles.

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Geometry 5.7

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  1. Geometry 5.7 The Pythagorean Theorem

  2. Learning Targets • Students will be able to… • Use the Pythagorean theorem and its converse to solve problems. • Use Pythagorean inequalities to classify triangles.

  3. Warm-up

  4. Homework Check

  5. Homework Check

  6. Vocabulary c a b

  7. Right Triangles Hypotenuse – Always the longest side. - Side opposite the right angle. - Side c is the hypotenuse Pythagorean Theorem: c a b Leg – The two shorter sides. - The sides that make up the right angle. - a and b are the legs

  8. Example Type 1: Using the Pythagorean Theorem Find the value of x

  9. Example Type 1: Using the Pythagorean Theorem Find the value of x

  10. Pythagorean Triples • Pythagorean Triples – all sides of the right triangle are whole numbers. • Still use the Pythagorean theorem to find the missing side. • However, when done if you notice that all three numbers are whole numbers then you have a Pythagorean triple. • 3, 4, 5 is a Pythagorean triple and any number times 3, 4, and 5 will create a Pythagorean triple.

  11. Example 2: Identifying Pythagorean Triples • Find the missing side. Tell if the side lengths form a Pythagorean Triple

  12. Example 2: Identifying Pythagorean Triples Find the missing side. Tell if the side lengths form a Pythagorean Triple

  13. Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • Step 1: Determine if a triangle • Step 2: Classify the triangle • Classify the triangle using the following chart

  14. Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • A. 8, 11, 13 B. 7, 12, 16

  15. Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • C. 5.8, 9.3, 15.6 D. 3.8, 4.1, 5.2

  16. Classifying Triangles • Tell if the measures can be the side lengths of a triangle. If so classify the triangle. • E. 5, 7, 10 F. 11, 18, 34

  17. Extra Practice 5.7

  18. Extra Practice 5.7

  19. Extra Practice 5.7

  20. Extra Practice 5.7

  21. Extra Practice 5.7

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