Two Special Right Triangles

1. Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90° HW: Special Right Triangles WS1 (side 1 only: 45-45-90)

2. 1 1 1 1 45°- 45°- 90° The 45-45-90 triangle is based on the square with sides of 1 unit.

3. 1 1 1 1 45°- 45°- 90° If we draw the diagonals we form two 45-45-90 triangles. 45° 45° 45° 45°

4. 1 1 1 1 45°- 45°- 90° Using the Pythagorean Theorem we can find the length of the diagonal. 45° 45° 45° 45°

5. 1 1 1 1 45°- 45°- 90° 45° 45° 2 45° 45°

6. 45° 1 45° 1 45°- 45°- 90°

7. In a 45° – 45° – 90° triangle the hypotenuse is the square root of two times as long as each leg Rule:

8. 45° 4 45° 45°- 45°- 90° Practice 4 SAME

9. 45° 9 45° 45°- 45°- 90° Practice 9 SAME

10. 45° 45° 45°- 45°- 90° Practice SAME

11. 45°- 45°- 90° Practice Now Let's Go Backward

12. 45° 45° 45°- 45°- 90° Practice

13. 45°- 45°- 90° Practice = 3

14. 45° 45° 45°- 45°- 90° Practice 3 3 SAME

15. 45° 45° 45°- 45°- 90° Practice

16. 45°- 45°- 90° Practice = 11

17. 45° 45° 45°- 45°- 90° Practice 11 11 SAME

18. 45° 45° 45°- 45°- 90° Practice 8

19. 8 = * 2 45°- 45°- 90° Practice Rationalize the denominator

20. 45° 45° 45°- 45°- 90° Practice 8 SAME

21. 45° 45° 45°- 45°- 90° Practice 4

22. 4 = * 2 45°- 45°- 90° Practice Rationalize the denominator

23. 45° 45° 45°- 45°- 90° Practice 4 SAME

24. 45° 45° 45°- 45°- 90° Practice 7

25. 7 * 45°- 45°- 90° Practice Rationalize the denominator

26. 45° 45° 45°- 45°- 90° Practice 7 SAME

27. Find the value of each variable. Write answers in simplest radical form.

28. Find the value of each variable. Write the answers in simplest radical form. • Know the basic triangles • Set known information equal to the corresponding part of the basic triangle • Solve for the other sides

29. Find the value of each variable. Write answers in simplest radical form.

31. Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90° HW: Special Right Triangles WS1 (side 2 only: 30-60-90)

32. 2 2 60° 60° 2 30°- 60°- 90° The 30-60-90 triangle is based on an equilateral triangle with sides of 2 units.

33. 2 2 60° 60° 2 30°- 60°- 90° The altitude cuts the triangle into two congruent triangles. 30° 30° 1 1

34. 30° 60° 30°- 60°- 90° This creates the 30-60-90 triangle with a hypotenuse a short leg and a long leg. Long Leg hypotenuse Short Leg

35. 30° 60° 30°- 60°- 90° Practice We saw that the hypotenuse is twice the short leg. 2 We can use the Pythagorean Theorem to find the long leg. 1

36. 30° 60° 30°- 60°- 90° Practice 2 1

37. 30° 60° 30°- 60°- 90° 2 1

38. 30° – 60° – 90° Triangle In a 30° – 60° – 90° triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of three times as long as the shorter leg

39. 30°-60°-90°

40. 30° 60° 30°- 60°- 90° Practice The key is to find the length of the short side. 8 Hypotenuse = short leg * 2 4

41. 30° 60° 30°- 60°- 90° Practice 10 5 hyp = short leg * 2

42. 30° 60° 30°- 60°- 90° Practice 14 7 * 2

43. 30° 60° 30°- 60°- 90° Practice 3 * 2

44. 30° 60° 30°- 60°- 90° Practice * 2

45. 30°- 60°- 90° Practice Now Let's Go Backward

46. 30° 60° 30°- 60°- 90° Practice 22 Short Leg = hyp2 11

47. 30° 60° 30°- 60°- 90° Practice 4 2

48. 30° 60° 30°- 60°- 90° Practice 18 9

49. 30° 60° 30°- 60°- 90° Practice 46 23

50. 30° 60° 30°- 60°- 90° Practice 28 14