1. Lesson 8-4 Special Right Triangles (page 300) Essential Question What is so special about the special right triangles?

2. Special Right Triangles The theorems presented here will provide short cuts to finding sides of special right triangles, BUT DO NOT FORGET the Pythagorean Theorem!

3. In a 45º - 45º - 90º triangle, the hypotenuse is times as long as a leg. Theorem 8-6 a ____ a Note: A 45º - 45º - 90º ∆ is an isosceles right ∆ with congruent legs. 45º

4. hypotenuse = leg x = _______ a a 45º

5. Example 1 (a): Find the length of the hypotenuse in the 45º-45º-90º∆. legs = 5 … hypotenuse = ______ hypotenuse = leg

6. Example 1 (b): Find the length of the hypotenuse in the 45º-45º-90º∆. legs = … hypotenuse = ____ hypotenuse = leg

7. Example 1 (c): Find the length of the hypotenuse in the 45º-45º-90º∆. legs = … hypotenuse = _____ hypotenuse

8. Example 1 (d): Find the length of the legs in the 45º-45º-90º∆. hypotenuse = … legs = ____ hypotenuse = leg

9. Example 1 (e): Find the length of the legs in the 45º-45º-90º∆. hypotenuse = 10 … legs = _____ hypotenuse = leg

10. Example 1 (f): Find the length of the legs in the 45º-45º-90º∆. hypotenuse = … legs = _____ hypotenuse = leg

11. In a 45º - 45º - 90º triangle, the hypotenuse is times as long as a leg. Theorem 8-6 a a Note: The ratio of the sides is: a : a: a or 1 : 45º

12. Assignment Worksheet on 45º-45º-90º Triangles hypotenuse = leg What is so special about the special right triangles?

13. In a 30º - 60º - 90º triangle, the hypotenuse is twice as long as the shorter leg, & the longer leg is times as long as the shorter leg. Theorem 8-7 b A a The shorter leg is opposite the 30º angle and the longer leg is opposite the 60º angle. c B C 30º 60º

14. b A a c B C 30º 60º 30º - 60º - 90º triangle short leg long leg hypotenuse

15. hypotenuse = 2 short leg b A a c B C 30º 60º long leg = short leg shorter leg = a hypotenuse = c = 2a longer leg = b = a

16. hypotenuse = 2 short leg A a 2 a B C 30º 60º long leg = short leg It is a Right Triangle!

17. Example 2 (a): Find the other 2 sides of the 30º-60º-90º∆. shorter leg = 2 hypotenuse = ______ longer leg = ________ hypotenuse = 2 short leg long leg = short leg

18. Example 2 (b): Find the other 2 sides of the 30º-60º-90º∆. hypotenuse = 12 shorter leg = ______ longer leg = ________ hypotenuse = 2 short leg long leg = short leg

19. Example 2 (c): Find the other 2 sides of the 30º-60º-90º∆. longer leg = shorter leg = ______ hypotenuse = ________ hypotenuse = 2 short leg long leg = short leg

20. In a 30º - 60º - 90º triangle, the hypotenuse is twice as long as the shorter leg, & the longer leg is times as long as the shorter leg. Theorem 8-7 A a Note: The ratio of the sides is: a : a : 2a or 1 : : 2 B C 30º 60º 2 a

21. Assignment Worksheet on 30º-60º-90º Triangles hypotenuse = 2 short leg long leg = short leg What is so special about the special right triangles?

22. In a 45º - 45º - 90º triangle, the hypotenuse is times as long as a leg. Theorem 8-6 a a Note: The ratio of the sides is: a : a: a or 1 : 45º

23. In a 30º - 60º - 90º triangle, the hypotenuse is twice as long as the shorter leg, & the longer leg is times as long as the shorter leg. Theorem 8-7 A a Note: The ratio of the sides is: a : a : 2a or 1 : : 2 B C 30º 60º 2 a

24. Assignment Written Exercises on pages 302 & 303 GRADED: 1 to 27 odd numbers ~ #32 BONUS! ~ Prepare for Quiz on Lessons 8-3 & 8-4 What is so special about the special right triangles?

25. Prepare for Quiz on Lessons 8-3 & 8-4 30º-60º-90º ∆ hypotenuse = 2 short leg long leg = short leg 45º-45º-90º ∆ hypotenuse = leg What is so special about the special right triangles?