9.3 pythagorean theorem day 2
- 1. Day Two
- 2. EXAMPLE 3 Identifying Right Triangles Use the converse of the Pythagorean Theorem to determine whether a triangle with the given side lengths is a right triangle. a. a = 6, b = 8, c = 10 a 2 + b 2 c 2 = ? 6 2 + 8 2 10 2 = ? 36 + 64 100 = ? ANSWER A right triangle b. a = 10, b = 12, c = 16 a 2 + b 2 c 2 = ? 10 2 + 12 2 16 2 = ? 100 + 144 256 = ? ANSWER Not a right triangle 100 = 100 244 = 256
- 3. Do these lengths make a right triangle? 28, 45, 53 2. 16, 18, 20 a 2 + b 2 = c 2 28 2 + 45 2 = 53 2 784 + 2025 = 2809 2809 = 2809 Yes a 2 + b 2 = c 2 16 2 + 18 2 = 20 2 256 + 324 = 400 580 = 400 No
- 4. Do these lengths make a right triangle? 25, 15, 20 4. 9, 41, 36 a 2 + b 2 = c 2 15 2 + 20 2 = 25 2 225 + 400 = 625 625 = 625 Yes a 2 + b 2 = c 2 9 2 + 36 2 = 41 2 81 + 1296 = 1681 1377 = 1681 No
- 5. EXAMPLE 2 Standardized Test Practice SOLUTION c 2 - a 2 = b 2 300 2 - 200 2 = b 2 90,000 – 40,000 = b 2 50,000 = b 2 Pythagorean Theorem Substitute 200 for a and 300 for c . Evaluate powers. Subtract. Take positive square root of each side. Approximate square root. 50,000 = b 2 b 223.6
- 6. EXAMPLE 2 Standardized Test Practice ANSWER You are about 224 feet above the water. The correct answer is B.
- 7. When you have a word problem dealing with the Pythagorean Theorem, it is always a good idea to draw a picture. Then you can visualize what is being discussed in the problem and label the correct parts. Try it!!
- 8. Eric is hiking from a camp site to the lake. He walks 3.5 miles directly south, then 4 miles directly east to get to the water. If the ground is flat, how much shorter is it if he walks in a straight line (instead of the route Eric took)? 3.5 S 4 E ??? Campsite Lake N E S W
- 9. 3.5 2 + 4 2 = _c 2 _ 12.25 + 16 = c 2 28.25 = c 2 About 5.3 miles = C So instead of walking 7.5 miles, he could have walked about 5.3 miles and saved 2.2 miles.
- 10. Homework Assignment: P. 485 #11 – 26, 30 – 33 Show your work for ALL problems . Round to the nearest tenth if needed. 3 points for each problem. Formula Substitute Answer