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# 7.1 apply the pythagorean theorem

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### 7.1 apply the pythagorean theorem

1. 1. 7.1 Apply the Pythagorean Theorem 7.1 Video attached Bell Thinger 1. Solve x2 = 100. ANSWER 10, –10 4. Find x. 2. Solve x2 + 9 = 25. ANSWER 4, –4 3. Simplify 20. ANSWER 2 5 ANSWER 6 cm
2. 2. 7.1
3. 3. Example 1 7.1 Find the length of the hypotenuse of the right triangle. SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem x 2 = 62 + 82 Substitute. x2 = 36 + 64 Multiply. x2 = 100 Add. x = 10 Find the positive square root.
4. 4. Guided Practice 7.1 Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form. 1. ANSWER Leg; 4
5. 5. Guided Practice 7.1 Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form. 2. ANSWER hypotenuse; 2 13
6. 6. Example 2 7.1 SOLUTION = +
7. 7. Example 2 7.1 162 = 42 + x2 Substitute. 256 = 16 + x2 Multiply. 240 = x2 Subtract 16 from each side. √240 = x Find positive square root. 15.492 ≈ x Approximate with a calculator. The ladder is resting against the house at about 15.5 feet above the ground. ANSWER The correct answer is D.
8. 8. Guided Practice 7.1 3. The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? ANSWER about 23.8 ft
9. 9. Guided Practice 7.1 4. The Pythagorean Theorem is only true for what type of triangle? ANSWER right triangle
10. 10. Example 3 7.1 Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. SOLUTION STEP 1 Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown.
11. 11. Example 3 7.1 STEP 2 Use the Pythagorean Theorem to find the height of the triangle. c2 = a2 + b2 Pythagorean Theorem Substitute. 132 = 52 + h2 Multiply. 169 = 25 + h2 Subtract 25 from each side. 144 = h2 12 = h Find the positive square root. STEP 3 Find the area. 1 Area = 1 (base) (height) = (10) (12) = 60 m2 2 2 The area of the triangle is 60 square meters.
12. 12. Guided Practice 7.1 Find the area of the triangle. 5. ANSWER about 149.2 ft2
13. 13. Guided Practice 7.1 Find the area of the triangle. 6. ANSWER 240 m2.
14. 14. 7.1
15. 15. Example 4 7.1 Find the length of the hypotenuse of the right triangle. SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of this triangle: 5 . 2 = 10 and 12. 2 = 24. So, the length of the hypotenuse is 13 . 2 = 26.
16. 16. Example 4 7.1 Method 2: Use the Pythagorean Theorem. x2 = 102 + 242 Pythagorean Theorem x2 = 100 + 576 Multiply. x2 = 676 Add. x = 26 Find the positive square root.
17. 17. Guided Practice 7.1 Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple. 7. ANSWER 15 in.
18. 18. Guided Practice 7.1 Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple. 8. ANSWER 50 cm.
19. 19. Exit Slip 7.1 1. Find the length of the hypotenuse of the right triangle. ANSWER 39
20. 20. Exit Slip 7.1 2. Find the area of the isosceles triangle. ANSWER 1080 cm2