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NY-10

Using the Pythagorean Theorem. NY-10. Lesson Presentation. Holt Course 2. Objective. Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator. c. a 2 + b 2 = c 2. a. b.

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NY-10

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  1. Using the Pythagorean Theorem NY-10 Lesson Presentation Holt Course 2

  2. Objective Determine whether a given triangle is a right triangle by applying the Pythagorean Theorem and using a calculator.

  3. c a2 + b2 = c2 a b The Pythagorean Theorem states that in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The Pythagorean Theorem also works in “reverse.” If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the remaining side, then the triangle is a right triangle.

  4. Example 1A: Determining if a Triangle is a Right Triangle The side lengths of a triangle are shown. Determine whether the triangle is a right triangle. 13 ft, 17 ft, 21 ft ? a2 + b2 = c2 Compare a2 + b2 = c2. Substitute the longest side length for c. ? 132 + 172 = 212 458441 Use a calculator. The triangle is not a right triangle.

  5. Example 1B: Determining if a Triangle is a Right Triangle The side lengths of a triangle are shown. Determine whether the triangle is a right triangle. 20 ft, 21 ft, 29 ft ? a2 + b2 = c2 Compare a2 + b2 = c2. Substitute the longest side length for c. ? 202 + 212 = 292 841=841 Use a calculator. The triangle is a right triangle.

  6. Check It Out! Example 1A The side lengths of a triangle are shown. Determine whether the triangle is a right triangle. 9 cm, 40 cm, 41 cm ? a2 + b2 = c2 Compare a2 + b2 = c2. Substitute the longest side length for c. ? 92 + 402 = 412 1681=1681 Use a calculator. The triangle is a right triangle.

  7. Check It Out! Example 1B The side lengths of a triangle are shown. Determine whether the triangle is a right triangle. 5 ft, 18 ft, 19 ft ? a2 + b2 = c2 Compare a2 + b2 = c2. Substitute the longest side length for c. ? 52 + 182 = 192 349 361 Use a calculator. The triangle is not a right triangle.

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