1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 8–2) Then/Now Theorem 8.8: 45°-45°-90° Triangle Theorem Example 1:Find the Hypotenuse Length in a 45°-45°-90° Triangle Example 2:Find the Leg Lengths in a 45°-45°-90° Triangle Theorem 8.9: 30°-60°-90° Triangle Theorem Example 3:Find Lengths in a 30°-60°-90° Triangle Example 4:Real-World Example: Use Properties of Special Right Triangles

3. Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 1 Find x. A.5 B. C. D.10.5

4. Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 2 Find x. A. B. C.45 D.51

5. Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 4 A.yes, acute B.yes, obtuse C.yes, right D.no Determine whether the set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. 16, 30, 33

6. Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 5 A.yes, acute B.yes, obtuse C.yes, right D.no Determine whether the set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right.

7. Over Lesson 8–2 A.A B.B C.C D.D 5-Minute Check 6 Which of the following are the lengths of an acute triangle? A.25, 20, 15 B.4, 7, 8 C.0.7, 2.4, 2.5 D.36, 48, 62 __ 1 2

8. Then/Now You used properties of isosceles and equilateral triangles. (Lesson 4–6) Use the properties of 45°-45°-90° triangles. Use the properties of 30°-60°-90° triangles.

9. Concept

10. Example 1 Find the Hypotenuse Length in a 45°-45°-90° Triangle A. Find x. The given angles of this triangle are 45° and 90°. This makes the third angle 45°, since 180 – 45 – 90 = 45. Thus, the triangle is a 45°-45°-90° triangle.

11. Example 1 Find the Hypotenuse Length in a 45°-45°-90° Triangle Substitution 45°-45°-90° Triangle Theorem

12. Example 1 Find the Hypotenuse Length in a 45°-45°-90° Triangle B. Find x. The legs of this right triangle have the same measure, x, so it is a 45°-45°-90° triangle. Use the 45°-45°-90° Triangle Theorem.

13. Example 1 Find the Hypotenuse Length in a 45°-45°-90° Triangle Substitution 45°-45°-90° Triangle Theorem x = 12 Answer: x = 12

14. A.A B.B C.C D.D Example 1 A. Find x. A.3.5 B.7 C. D.

15. A.A B.B C.C D.D Example 1 B. Find x. A. B. C.16 D.32

16. Example 2 Find the Leg Lengths in a 45°-45°-90° Triangle Find a. The length of the hypotenuse of a 45°-45°-90° triangle is times as long as a leg of the triangle. Substitution 45°-45°-90° Triangle Theorem

17. Example 2 Find the Leg Lengths in a 45°-45°-90° Triangle Multiply. Divide. Rationalize the denominator. Divide each side by

18. A.A B.B C.C D.D Example 2 Find b. A. B.3 C. D.

19. Concept

20. Example 3 Find Lengths in a 30°-60°-90° Triangle Find x and y. The acute angles of a right triangle are complementary, so the measure of the third angle is 90 – 30 or 60. This is a 30°-60°-90° triangle.

21. Example 3 Find Lengths in a 30°-60°-90° Triangle Find the length of the longer side. Substitution Simplify. 30°-60°-90° Triangle Theorem

22. Example 3 Find Lengths in a 30°-60°-90° Triangle Find the length of hypotenuse. Substitution Simplify. 30°-60°-90° Triangle Theorem Answer: x = 4,

23. A.A B.B C.C D.D Example 3 Find BC. A.4 in. B.8 in. C. D.12 in.

24. A.A B.B C.C D.D Example 4 BOOKENDS Shaina designed 2 identical bookends according to the diagram below. Use special triangles to find the height of the bookends. A. B.10 C.5 D.

25. End of the Lesson