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5-Minute Check on Lesson 7-1

Transparency 7-2. 5-Minute Check on Lesson 7-1. Find the geometric mean between each pair of numbers. State exact answers and answers to the nearest tenth. 9 and 13 2. 2√5 and 5√5

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5-Minute Check on Lesson 7-1

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  1. Transparency 7-2 5-Minute Check on Lesson 7-1 • Find the geometric mean between each pair of numbers. State exact answers and answers to the nearest tenth. • 9 and 13 2. 2√5 and 5√5 • 3. Find the altitude 4. Find x, y, and z • 5. Which of the following is the best estimate of x? √50 ≈ 7.1 √117 ≈ 10.8 x = 8, y = √80 ≈ 8.9 z = √320 ≈ 17.9 z y x 8 3 4 √24 ≈ 4.9 20 13 Standardized Test Practice: x 5 12 A B C D 12 2 10 11 C Click the mouse button or press the Space Bar to display the answers.

  2. Lesson 7-2 Pythagorean Theorem and its Converse

  3. Objectives • Use the Pythagorean Theorem • If a right triangle, then c² = a² + b² • Use the converse of the Pythagorean Theorem • If c² = a² + b², then a right triangle

  4. Vocabulary • None new

  5. Pythagorean Theorem Pythagorean Theorem a2 + b2 = c2 Sum of the squares of the legs is equalto the square of the hypotenuse c a b Converse of the Pythagorean Theorem: If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle Remember from our first computer quiz: In an acute triangle, c2 < a2 + b2. In an obtuse triangle, c2 > a2 + b2.

  6. Answer: Example 1 Find d. Pythagorean Theorem Simplify. Subtract 9 from each side. Take the square root of each side. Use a calculator.

  7. Answer: Example 2 Find x.

  8. Pythagorean Triples For three numbers to be a Pythagorean triple they must satisfy both of the following conditions: • They must satisfy c2 = a2 + b2where c is the largest number • All three must be whole numbers (integers) Common Pythagorean Triples: 3, 4, 55, 12, 138, 15, 17 6, 8, 10 9, 12, 15 7, 24, 25 12, 16, 20 9, 40, 41 15, 20, 25 10, 24, 26 16, 30, 34

  9. Example 3 Determine whether 9, 12, and 15are the sides of a right triangle. Then state whether they form a Pythagorean triple. Since the measure of the longest side is 15, 15 must be c. Let a and b be 9 and 12. Pythagorean Theorem Simplify. Add. Answer: These segments form the sides of a right triangle since they satisfy the Pythagorean Theorem. The measures are whole numbers and form a Pythagorean triple.

  10. Answer: Since , segments with these measures cannot form a right triangle. Therefore, they do not form a Pythagorean triple. Example 4 Determine whether 21, 42, and 54are the sides of a right triangle. Then state whether they form a Pythagorean triple. Pythagorean Theorem Simplify. Add.

  11. Determine whether 4, and 8 are the sides of a right triangle. Then state whether they form a Pythagorean triple. Answer: Since 64 = 64, segments with these measures form a right triangle. However, is not a whole number. Therefore, they do not form a Pythagorean triple. Example 5 Pythagorean Theorem Simplify. Add.

  12. Determine whether each set of measures are the sides of a right triangle. Then state whether they form a Pythagorean triple. a. 6, 8, 10b. 5, 8, 9c. Example 6 Answer: The segments form the sides of a right triangle and the measures form a Pythagorean triple. Answer: The segments do not form the sides of a right triangle,and the measuresdo not forma Pythagorean triple. Answer: The segments form the sides of a right triangle, but the measures do not form a Pythagorean triple.

  13. Summary & Homework • Summary: • The Pythagorean Theorem can be used to find the measures of the sides of a right triangle • If the measures of the sides of a triangle form a Pythagorean triple, then the triangle is a right triangle • Homework: • pg 354, 17-19, 22-25, 30-35

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