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

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

3. Holt Course 2 NY-10 Using the Pythagorean Theorem 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. a 2 + b 2 = c 2 a c b

4. Holt Course 2 NY-10 Using the Pythagorean Theorem 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. The triangle is not a right triangle. 13 ft, 17 ft, 21 ft Compare a 2 + b 2 = c 2. Substitute the longest side length for c. Use a calculator. a 2 + b 2 = c 2 13 2 + 17 2 = 21 2 458  441 ? ?

5. Holt Course 2 NY-10 Using the Pythagorean Theorem 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. The triangle is a right triangle. 20 ft, 21 ft, 29 ft Compare a 2 + b 2 = c 2. Substitute the longest side length for c. Use a calculator. a 2 + b 2 = c 2 20 2 + 21 2 = 29 2 841 = 841 ? ?

6. Holt Course 2 NY-10 Using the Pythagorean Theorem 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 The triangle is a right triangle. Compare a 2 + b 2 = c 2. Substitute the longest side length for c. Use a calculator. a 2 + b 2 = c 2 9 2 + 40 2 = 41 2 1681 = 1681 ? ?

7. Holt Course 2 NY-10 Using the Pythagorean Theorem 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 The triangle is not a right triangle. Compare a 2 + b 2 = c 2. Substitute the longest side length for c. Use a calculator. a 2 + b 2 = c 2 5 2 + 18 2 = 19 2 349  361 ? ?