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

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

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

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

5. 45°- 45°- 90° 1
45°
45° 2
45°
45°

6. 45°- 45°- 90° 1
45°

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

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

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

10. 45°- 45°- 90° Practice 2
45° 2
SAME

11. 45°- 45°- 90° Practice
45°
SAME

12. 45°- 45°- 90° Practice
Now Let's
Go Backward

13. 45°- 45°- 90° Practice
45°

14. 45°- 45°- 90° Practice
= 3

15. 45°- 45°- 90° Practice
45° 3 3
SAME

16. 45°- 45°- 90° Practice
45°

17. 45°- 45°- 90° Practice
= 6

18. 45°- 45°- 90° Practice
45° 6 6
SAME

19. 45°- 45°- 90° Practice
45°

20. 45°- 45°- 90° Practice
= 11

21. 45°- 45°- 90° Practice
45° 11 11
SAME

22. 45°- 45°- 90° Practice
45° 8

23. 45°- 45°- 90° Practice 8 * = 2
Rationalize the denominator

24. 45°- 45°- 90° Practice
45° 8
SAME

25. 45°- 45°- 90° Practice
45° 4

26. 45°- 45°- 90° Practice 4 * = 2
Rationalize the denominator

27. 45°- 45°- 90° Practice
45° 4
SAME

28. 45°- 45°- 90° Practice
45° 7

29. 45°- 45°- 90° Practice 7 *
Rationalize the denominator

30. 45°- 45°- 90° Practice
45° 7
SAME

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

32. 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

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

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

36. 30°- 60°- 90°
The triangle is based on an equilateral triangle with sides of 2 units. 2
60°

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

38. 30°- 60°- 90°
This creates the triangle with a hypotenuse a short leg and a long leg.
30°
60°
Long Leg
hypotenuse
Short Leg

39. 30°- 60°- 90° Practice
We saw that the hypotenuse is twice the short leg.
60°
30° 2
We can use the Pythagorean Theorem to find the long leg. 1

40. 30°- 60°- 90° Practice
60°
30° 2 1

41. 30°- 60°- 90°
60°
30° 2 1

42. 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

43. 30°-60°-90°

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

45. 30°- 60°- 90° Practice
60°
30° 10 5
hyp =
short leg * 2

46. 30°- 60°- 90° Practice
60°
30° 14 7
* 2

47. 30°- 60°- 90° Practice
60°
30° 3
* 2

48. 30°- 60°- 90° Practice
60°
30°
* 2

49. 30°- 60°- 90° Practice
Now Let's
Go Backward

50. 30°- 60°- 90° Practice
60°
30° 22
Short Leg = hyp 2 11

51. 30°- 60°- 90° Practice
60°
30° 4 2

52. 30°- 60°- 90° Practice
60°
30° 18 9

53. 30°- 60°- 90° Practice
60°
30° 46 23

54. 30°- 60°- 90° Practice
60°
30° 28 14

55. 30°- 60°- 90° Practice
60°
30° 9

57. 30°- 60°- 90° Practice
60°
30° 12
hyp =
Short Leg * 2

58. 30°- 60°- 90° Practice
60°
30° 27
hyp =
Short Leg * 2

59. 30°- 60°- 90° Practice
60°
30° 20
hyp =
Short Leg * 2

60. 30°- 60°- 90° Practice
60°
30° 33
hyp =
Short Leg * 2

61. Find all the missing sides for each triangle.
PRACTICE
Find all the missing sides for
each triangle.

62. Solving Strategy Know the basic triangles
Set known information equal to the corresponding part of the basic triangle
Solve for the other sides

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

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

67. 5.5
5.5
5.5

68. 10 10 10

70. 10 10 5 10

78. 8

79. 2

81. Find the distance across the canyon. b

82. Find the length of the canyon wall (from the edge to the river).b
c = b * 2 c

83. Is it more or less than a mile across the canyon?
5280 ft = 1 mile

84. THE END