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The Pythagorean Theorem Warm UP Get a slip of paper from the chair. Follow

The Pythagorean Theorem Warm UP Get a slip of paper from the chair. Follow the directions and answer the questions.

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem 6 -1 The Pythagorean Theorem Proof Video

The Pythagorean Theorem 6 -1 The Pythagorean Theorem Proof Video

The Pythagorean Theorem Review Find each value to the nearest tenth. 1. 2. 3.

The Pythagorean Theorem Review Find each value to the nearest tenth. 1. 2. 3. 4.

The Pythagorean Theorem • Essential Question • Standard How can you use the MCC

The Pythagorean Theorem • Essential Question • Standard How can you use the MCC 8. G. 7: Apply the Pythagorean Theorem to solve problems? to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

The Pythagorean Theorem Vocabulary Pythagorean Theorem leg hypotenuse

The Pythagorean Theorem Vocabulary Pythagorean Theorem leg hypotenuse

The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos. He is

The Pythagorean Theorem Pythagoras was born on the Aegean island of Samos. He is best known for the Pythagorean Theorem, which relates the side lengths of a right triangle.

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem Additional Example 1 A: Finding the Length of a Hypotenuse Find

The Pythagorean Theorem Additional Example 1 A: Finding the Length of a Hypotenuse Find the length of the hypotenuse to the nearest hundredth. c 4 5 a 2 + b 2 = c 2 42 + 5 2 = c 2 16 + 25 = c 2 41 = c 6. 40 c Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

The Pythagorean Theorem Helpful Hint When using the Pythagorean Theorem to find length, use

The Pythagorean Theorem Helpful Hint When using the Pythagorean Theorem to find length, use only the principal square root.

The Pythagorean Theorem Check It Out: Example 1 A Find the length of the

The Pythagorean Theorem Check It Out: Example 1 A Find the length of the hypotenuse to the nearest hundredth. c 5 7 a 2 + b 2 = c 2 52 + 7 2 = c 2 25 + 49 = c 2 74 = c 8. 60 c Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

The Pythagorean Theorem Additional Example 2: Finding the Length of a Leg in a

The Pythagorean Theorem Additional Example 2: Finding the Length of a Leg in a Right Triangle Solve for the unknown side in the right triangle to the nearest tenth. 25 7 a 2 + b 2 = c 2 b 72 + b 2 = 252 49 + b 2 = 625 – 49 b 2 = 576 b = 24 Pythagorean Theorem Substitute for a and c. Simplify powers. Subtract 49 from each side. Find the positive square root.

The Pythagorean Theorem Additional Example 3: Using the Pythagorean Theorem for Measurement Two airplanes

The Pythagorean Theorem Additional Example 3: Using the Pythagorean Theorem for Measurement Two airplanes leave the same airport at the same time. The first plane flies to a landing strip 350 miles south, while the other plane flies to an airport 725 miles west. How far apart are the two planes after they land? a 2 + b 2 = c 2 Pythagorean Theorem 3502 + 7252 = c 2 Substitute for a and b. 122, 500 + 525, 625 = c 2 Simplify powers. 648, 125 = c 2 Add. 805 ≈ c Find the positive square root. The two planes are approximately 805 miles apart.

The Pythagorean Theorem Check It Out: Example 1 B Find the length of the

The Pythagorean Theorem Check It Out: Example 1 B Find the length of the hypotenuse to the nearest hundredth. triangle with coordinates (– 2, – 2), (– 2, 4), and (3, – 2) (– 2, 4) y The points form a right triangle. x (– 2, – 2) (3, – 2) a 2 + b 2 = c 2 62 + 5 2 = c 2 36 + 25 = c 2 61 = c 7. 81 c Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

The Pythagorean Theorem Additional Example 1 B: Finding the Length of a Hypotenuse Find

The Pythagorean Theorem Additional Example 1 B: Finding the Length of a Hypotenuse Find the length of the hypotenuse to the nearest hundredth. triangle with coordinates (1, – 2), (1, 7), and (13, – 2) a 2 + b 2 92 + 122 81 + 144 225 15 = = = c 2 c 2 c c Pythagorean Theorem Substitute for a and b. Simplify powers. Solve for c; c = c 2.

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem Workbook Pg. 142 Scan for answers Review Video

The Pythagorean Theorem Workbook Pg. 142 Scan for answers Review Video

The Pythagorean Theorem Day 2 Review 1. Find the height h of the triangle.

The Pythagorean Theorem Day 2 Review 1. Find the height h of the triangle. 8 m 2. Find the length of side c to the nearest meter. 12 m c 10 m h 6 m 9 m

The Pythagorean Theorem • Essential Question • Standard How can you use the MCC

The Pythagorean Theorem • Essential Question • Standard How can you use the MCC 8. G. 7: Apply the Pythagorean Theorem to solve problems? to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

The Pythagorean Theorem 6 -2 Applying the Pythagorean Theorem and Its Converse 1. Video

The Pythagorean Theorem 6 -2 Applying the Pythagorean Theorem and Its Converse 1. Video

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem Additional Example 1: Marketing Application What is the diagonal length of

The Pythagorean Theorem Additional Example 1: Marketing Application What is the diagonal length of the projector screen? Use the Pythagorean 72 + 3 2 = c 2 Theorem Simplify. 49 + 9 = c 2 58 = c 2 Add. 58 = c 7. 615 c The diagonal length should be given as about 7. 62 feet.

The Pythagorean Theorem Check It Out: Example 1 What is the diagonal length of

The Pythagorean Theorem Check It Out: Example 1 What is the diagonal length of the projector screen? Use the Pythagorean 2 + 8 2 = c 2 12 12 ft Theorem 2 Simplify. 8 ft 144 + 64 = c 208 = c 2 Add. 208 = c 14. 42 c The diagonal length should be given as about 14. 4 feet.

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem Workbook Practice Pg. 147 Scan to get answers Skip #9 for

The Pythagorean Theorem Workbook Practice Pg. 147 Scan to get answers Skip #9 for now

The Pythagorean Theorem Day 3

The Pythagorean Theorem Day 3

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

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