Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

Applying the Pythagorean Theorem and Its Converse 3-9 Warm Up Find the distance between each pair of points. 1. (8, 2) and (8, 7) ‏ 2. (–2, 4) and (5, 4) ‏ 3. (–1, –1) and (9, –1) ‏ 4. (–8, –4) and (–2, –4) ‏ 5 units 7 units 10 units 6 units

Applying the Pythagorean Theorem and Its Converse 3-9 Learn to use the Distance Formula and the Pythagorean Theorem and its converse to solve problems.

Applying the Pythagorean Theorem and Its Converse  c Use the Pythagorean Theorem Simplify = c = c 2 58 = c 2 58 = c Add. Example 1: Marketing Application A.What is the diagonal length of the projector screen? The diagonal length should be given as about 7.62 feet.

Applying the Pythagorean Theorem and Its Converse  c Use the Pythagorean Theorem Simplify = c = c = c = c Add. Check It Out B. What is the diagonal length of the projector screen? The diagonal length should be given as about 14.4 feet. 12 ft 8 ft

Applying the Pythagorean Theorem and Its Converse 3-9

Applying the Pythagorean Theorem and Its Converse 3-9 Use the Distance Formula. J and K Example 2: Finding Distance on the Coordinate Plane A. Find the distances between the points to the nearest tenth. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Additional Example 2A Continued Find the distances between the points to the nearest tenth. d = (0 – (–4))² + (–3 – 0 )² d = (4)² + (–3)² Simplify powers. d = The distance between A and B is 5 units.

Applying the Pythagorean Theorem and Its Converse 3-9 L and M Example 2: Finding Distance on the Coordinate Plane B. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Additional Example 2B Continued Find the distances between the points to the nearest tenth. d = (5 – 4)² + (–3 – 0)² d = (1)² + (–3)² Simplify powers. d = The distance between L and M is about 3.2 units.

Applying the Pythagorean Theorem and Its Converse 3-9 J and L Check It Out C. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example Continued Find the distances between the points to the nearest tenth. d = (4 – (–4))² + (0 – 0)² d = (8)² + (0)² Simplify powers. d = The distance between J and L is 8 units.

Applying the Pythagorean Theorem and Its Converse 3-9 K and M Check It Out D. Find the distances between the points to the nearest tenth. Use the Distance Formula. Let A be (x 1, y 1 )² and B be (x 2, y 2 )².

Applying the Pythagorean Theorem and Its Converse 3-9 Substitute. Subtract. Check It Out: Example D Continued Find the distances between the points to the nearest tenth. d = ((–4) – 0)² + (– 3 – (–3)² d = (–4)² + (0)² Simplify powers. d = The distance between K and M is 4 units.

Applying the Pythagorean Theorem and Its Converse 3-9 Problem of the Day The sum of the squares of two positive numbers is 100. One number is two more than the other. What are the numbers? 6 and 8

Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: Identifying a Right Triangle a 2 + b 2 = c = = = 225 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. A. Tell whether the given side lengths form a right triangle. 9, 12, 15 Simplify. Add.

Applying the Pythagorean Theorem and Its Converse 3-9 Example 3: Identifying a Right Triangle a 2 + b 2 = c = = ≠ 169 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. B. Tell whether the given side lengths form a right triangle. 8, 10, 13 Simplify. Add.

Applying the Pythagorean Theorem and Its Converse 3-9 Check It Out a 2 + b 2 = c = = ≠ 81 x Substitute. Compare a² + b² to c². The side lengths do not form a right triangle. C. Tell whether the given side lengths form a right triangle. 5, 6, 9 Simplify. Add.

Applying the Pythagorean Theorem and Its Converse 3-9 Example 3B a 2 + b 2 = c = = = 289 √ Substitute. Compare a² + b² to c². The side lengths form a right triangle. D. Tell whether the given side lengths form a right triangle. 8, 15, 17 Simplify. Add.

Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz

Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part I 1. width = 9 in., length = 40 in. 2. base length = 20 m, height = 15 m. 41 in. 25 m Find the length of the diagonal of the rectangle.

Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part II 3. Q and R 4. S and T ≈ 6.3 ≈ 2.2 Find the distance between the points to the nearest tenth.

Applying the Pythagorean Theorem and Its Converse 3-9 Lesson Quiz: Part III cm, 13 cm, 16 cm ft, 60 ft, 61 ft no yes Tell whether the given side lengths form a right triangle.