1. Warm-Up Exercises 2. Solve x 2 + 9 = 25. ANSWER 10, –10 ANSWER 4, –4 1. Solve x 2 = 100. ANSWER 2 5 3. Simplify 20.

2. Warm-Up Exercises ANSWER 6 cm 4. Find x.

3. Warm-Up Exercises Apply The Pythagorean Theorem Section 7.1

4. Warm-Up Exercises Standard and Objective Standard: G-3: The student will demonstrate through the mathematical processes an understanding of the properties and special segments of triangles and the relationships between and among triangles. Objective:G-3.10:Use the Pythagorean theorem and its converse to solve problems. Section 7.1

5. Warm-Up Exercises Apply the Pythagorean Theorem Section 7.1

6. Warm-Up Exercises EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean Theorem x 2 = 6 2 + 8 2 x 2 = 36 + 64 x 2 = 100 x = 10 Find the positive square root. Substitute. Multiply. Add.

7. Warm-Up Exercises GUIDED PRACTICE for Example 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

8. Warm-Up Exercises GUIDED PRACTICE for Example 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. hypotenuse; 213 ANSWER

9. Warm-Up Exercises EXAMPLE 2 Standardized Test Practice SOLUTION =+

10. Warm-Up Exercises EXAMPLE 2 Standardized Test Practice Find positive square root. Substitute. Multiply. Subtract 16 from each side. SOLUTION Approximate with a calculator. 16 2 = 4 2 + x 2 256 = 16 + x 2 15.492 ≈ x 240 = x 240 = x 2 ANSWER The ladder is resting against the house at about 15.5 feet above the ground. The correct answer is D.

11. Warm-Up Exercises GUIDED PRACTICE for Example 2 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? 3. about 23.8 ft ANSWER

12. Warm-Up Exercises GUIDED PRACTICE for Example 2 The Pythagorean Theorem is only true for what type of triangle? 4. right triangleANSWER

13. Warm-Up Exercises EXAMPLE 3 Find the area of an isosceles triangle SOLUTION Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. 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.

14. Warm-Up Exercises EXAMPLE 3 Find the area of an isosceles triangle Use the Pythagorean Theorem to find the height of the triangle. STEP 2 Pythagorean Theorem Substitute. Multiply. Subtract 25 from each side. Find the positive square root. c 2 = a 2 + b 2 12 = h 13 2 = 5 2 + h 2 169 = 25 + h 2 144 = h 2

15. Warm-Up Exercises EXAMPLE 3 Find the area of an isosceles triangle Find the area. STEP 3 = (10) (12) = 60 m 2 1 2 ANSWER The area of the triangle is 60 square meters. Area = 1 2 (base) (height)

16. Warm-Up Exercises GUIDED PRACTICE for Example 3 5. Find the area of the triangle. ANSWERabout 149.2 ft 2.

17. Warm-Up Exercises GUIDED PRACTICE for Example 3 Find the area of the triangle. 6. ANSWER 240 m 2.

18. Warm-Up Exercises Section 7.1

19. Warm-Up Exercises EXAMPLE 4 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. Find the length of a hypotenuse using two methods Find the length of the hypotenuse of the right triangle.

20. Warm-Up Exercises EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Method 2: Use the Pythagorean Theorem. x 2 = 10 2 + 24 2 x 2 = 100 + 576 x 2 = 676 x = 26 Pythagorean Theorem Multiply. Add. Find the positive square root.

21. Warm-Up Exercises GUIDED PRACTICE for Example 4 Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple. 7. ANSWER 15 in. 8. ANSWER 50 cm.

22. Warm-Up Exercises Daily Homework Quiz 1. Find the length of the hypotenuse of the right triangle. ANSWER 39

23. Warm-Up Exercises Daily Homework Quiz 2. Find the area of the isosceles triangle. ANSWER 1080 cm 2

24. Warm-Up Exercises Daily Homework Quiz 3. Find the unknown side length x. Write your answer in simplest radical form. ANSWER 413