2. * Students will Use the Converse of the Pythagorean Theorem to solve problems. * Use side lengths to classify triangles by their angle measures. * Why? So you can ascertain problems which require Right Triangles to determine side lengths. * Mastery is 80% or better on 5-min checks and indy work.

3. * In Lesson 7.1, you learned that if a triangle is a right triangle, then the square of the length of the hypotenuse is equal to the sum of the squares of the length of the legs. The Converse of the Pythagorean Theorem is also true, as stated on the following slide.

4. * If the square of the length of the longest side of the triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle. * If c 2 = a 2 + b 2, then ∆ABC is a right triangle.

5. *Y*Y ou can use the Converse of the Pythagorean Theorem to verify that a given triangle is a right triangle, as shown in Example 1.

6. * The triangles on the slides that follow appear to be right triangles. Tell whether they are right triangles or not. √113 4√95

7. * Let c represent the length of the longest side of the triangle. Check to see whether the side lengths satisfy the equation c 2 = a 2 + b 2. (√113) 2 = 7 2 + 8 2 113 = 49 + 64 113 = 113 ✔ √113 ? ? The triangle is a right triangle.

8. c 2 = a 2 + b 2. (4√95) 2 = 15 2 + 36 2 4 2 ∙ (√95) 2 = 15 2 + 36 2 16 ∙ 95 = 225+1296 1520 ≠ 1521 ✔ 4√95 The triangle is NOT a right triangle. ? ? ?

9. * Sometimes it is hard to tell from looking at a triangle whether it is obtuse or acute. The theorems on the following slides can help you tell.

10. * If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is acute. * If c 2 < a 2 + b 2, then ∆ABC is acute c 2 < a 2 + b 2

11. *I*I f the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse. *I*I f c 2 > a 2 + b 2, then ∆ABC is obtuse c 2 > a 2 + b 2

12. * Decide whether the set of numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute or obtuse. a. 38, 77, 86b. 10.5, 36.5, 37.5 You can use the Triangle Inequality to confirm that each set of numbers can represent the side lengths of a triangle. Compare the square o the length of the longest side with the sum of the squares of the two shorter sides.

13. Statement: c 2 ? a 2 + b 2 86 2 ? 38 2 + 77 2 7396 ? 1444 + 5929 7396 > 7373 Reason: Compare c 2 with a 2 + b 2 Substitute values Multiply c 2 is greater than a 2 + b 2 The triangle is obtuse

14. Statement: c 2 ? a 2 + b 2 37.5 2 ? 10.5 2 + 36.5 2 1406.25 ? 110.25 + 1332.25 1406.25 < 1442.5 Reason: Compare c 2 with a 2 + b 2 Substitute values Multiply c 2 is less than a 2 + b 2 The triangle is acute

15. * Page 444 * 2-22 all

16. * Construction: You use four stakes and string to mark the foundation of a house. You want to make sure the foundation is rectangular. a. A friend measures the four sides to be 30 feet, 30 feet, 72 feet, and 72 feet. He says these measurements prove that the foundation is rectangular. Is he correct?

17. *S*S olution: Your friend is not correct. The foundation could be a nonrectangular parallelogram, as shown below.

18. b. You measure one of the diagonals to be 78 feet. Explain how you can use this measurement to tell whether the foundation will be rectangular.

19. Solution: The diagonal divides the foundation into two triangles. Compare the square of the length of the longest side with the sum of the squares of the shorter sides of one of these triangles. * Because 900 + 5184 = 6084, you can conclude that both the triangles are right triangles. The foundation is a parallelogram with two right angles, which implies that it is rectangular

20. * Students will Use the Converse of the Pythagorean Theorem to solve problems. * Use side lengths to classify triangles by their angle measures. * Why? So you can ascertain problems which require Right Triangles to determine side lengths. * Mastery is 80% or better on 5-min checks and indy work.

21. * Pages 444-445 * #23-34 all…..due this period!