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Splash Screen. Five-Minute Check (over Lesson 3–4) Main Idea and Vocabulary Key Concept: Pythagorean Theorem Example 1: Find the Length of a Side Example 2: Find the Length of a Side Key Concept: Converse of Pythagorean Theorem Example 3: Identify a Right Triangle. Lesson Menu.

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–4) Main Idea and Vocabulary Key Concept: Pythagorean Theorem Example 1: Find the Length of a Side Example 2: Find the Length of a Side Key Concept: Converse of Pythagorean Theorem Example 3: Identify a Right Triangle Lesson Menu

  3. Use the Pythagorean Theorem. • legs • hypotenuse • Pythagorean Theorem • converse Main Idea/Vocabulary

  4. KC

  5. Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary. Find the Length of a Side Example 1

  6. c = Definition of square root Find the Length of a Side c2 = a2 +b2 Pythagorean Theorem c2 = 122 + 162 Replace a with 12 and b with 16. c2 = 144 + 256 Evaluate 122 and 162. c2 = 400 Add 144 and 256. c = 20 or –20 Simplify. Answer: The equation has two solutions, 20 and –20. However, the length of a side must be positive. So, the hypotenuse is 20 inches long. Example 1

  7. A B C D Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary. A.c2 = 82 + 152; 17 in. B.c2 = 152 – 82; 19 in. C. 152 = a2 + 82; 20 in. D. 152 = c2 – 82; 21 in. Example 1

  8. The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. What is a, the length of the other leg? = a Definition of square root Find the Length of a Side c2 = a2 +b2 Pythagorean Theorem 332 = a2 + 282 Replace c with 33 and b with 28. 1,089= a2 + 784 Evaluate 332 and 282. 1,089 – 784= a2 + 784 – 784 Subtract 784 from each side. 305 = a2 Simplify. 17.5 ≈ a Use a calculator. Example 2

  9. Find the Length of a Side Answer: The length of the other leg is about 17.5 centimeters. Example 2

  10. A B C D The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. What is a, the length of the other leg? A. about 16.2 cm B. about 18.5 cm C. about 19.7 cm D. about 21.4 cm Example 2

  11. KC

  12. The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. ? 252 = 72 + 242 Replace a with 7, b with 24, and c with 25. ? 625= 49 + 576 Evaluate 252, 72, and 242. Identify a Right Triangle c2 = a2 +b2 Pythagorean Theorem 625= 625 Simplify. Answer: The triangle is a right triangle. Example 3

  13. A B C The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle. A. It is a right triangle. B. It is not a right triangle. C. not enough information to determine Example 3

  14. End of the Lesson End of the Lesson

  15. Five-Minute Check (over Lesson 3–4) Image Bank Math Tools Square Roots The Pythagorean Theorem Resources

  16. A B C D (over Lesson 3-4) Name all sets of numbers to which the real number 286 belongs. A.rational, integer, whole number, real B. integer, irrational, rational, real C. integer, irrational, real D. irrational, real Five Minute Check 1

  17. A B C D Name all sets of numbers to which the real number belongs. (over Lesson 3-4) A. rational, real B. integer, real C. whole number, real D. irrational, real Five Minute Check 2

  18. A B C D Estimate to the nearest tenth. (over Lesson 3-4) A. 6 B. 5.8 C. 5 D. 2.9 Five Minute Check 3

  19. A B C D Estimate to the nearest tenth. (over Lesson 3-4) A. 16.6 B. 17 C. 17.9 D. 18 Five Minute Check 4

  20. A B C (over Lesson 3-4) Are irrational numbers sometimes, always, or never rational numbers? A. always B. sometimes C. never Five Minute Check 5

  21. A B C D To which set does not belong? (over Lesson 3-4) A. real B. rational C. fractions D. negative integers Five Minute Check 6

  22. End of Custom Shows

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