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Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90°

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Presentation on theme: "Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90°"— Presentation transcript:

1 Two Special Right Triangles 45°- 45°- 90° 30°- 60°- 90°

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

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

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

5 45°- 45°- 90° = c = c 2 2 = c 2  2 = c = c = c 2 2 = c 2  2 = c ° 22

6 45°- 45°- 90° Conclusion: the ratio of the sides in a triangle is 1-1-  2 Conclusion: the ratio of the sides in a triangle is 1-1-  22 45°

7 45°- 45°- 90° Practice 4 4  2 SAME leg*  °

8 45°- 45°- 90° Practice 9 9  2 SAME leg*  °

9 45°- 45°- 90° Practice 2 2  2 SAME leg*  °

10 45°- 45°- 90° Practice  14 SAME leg*  2 77 77 45°

11 45°- 45°- 90° Practice

12 3  2 hypotenuse   2 45°

13 45°- 45°- 90° Practice 3  2 22 = 3

14 45°- 45°- 90° Practice 3  2 hypotenuse   2 45° 3 SAME 3

15 45°- 45°- 90° Practice 6  2 hypotenuse   2 45°

16 45°- 45°- 90° Practice 6  2 22 = 6

17 45°- 45°- 90° Practice 6  2 hypotenuse   2 45° 6 SAME 6

18 45°- 45°- 90° Practice 11  2 hypotenuse   2 45°

19 45°- 45°- 90° Practice 11  2 22 = 11

20 45°- 45°- 90° Practice 11  2 hypotenuse   2 45° 11 SAME 11

21 45°- 45°- 90° Practice 8 hypotenuse   2 45°

22 45°- 45°- 90° Practice 8 22 22 22 * = 8282 2 = 4  2

23 45°- 45°- 90° Practice 8 hypotenuse   2 45° 4242 SAME 4242

24 45°- 45°- 90° Practice 4 hypotenuse   2 45°

25 45°- 45°- 90° Practice 4 22 22 22 * = 4242 2 = 2  2

26 45°- 45°- 90° Practice 4 hypotenuse   2 45° 2222 SAME 2222

27 45°- 45°- 90° Practice 6 Hypotenuse   2 45°

28 45°- 45°- 90° Practice 6 22 22 22 * = 6262 2 = 3  2

29 45°- 45°- 90° Practice 6 hypotenuse   2 45° 3232 SAME 3232

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

31 °- 60°- 90° The altitude (also the angle bisector and median) cuts the triangle into two congruent triangles. The altitude (also the angle bisector and median) cuts the triangle into two congruent triangles °

32 60 ° This creates the triangle with a hypotenuse a short leg and a long leg. This creates the triangle with a hypotenuse a short leg and a long leg. 30°- 60°- 90° hypotenuse Short Leg Long Leg

33 60° 30° 30°- 60°- 90° Practice 1 2 We saw that the hypotenuse is twice the short leg. We saw that the hypotenuse is twice the short leg. We can use the Pythagorean Theorem to find the long leg. We can use the Pythagorean Theorem to find the long leg.

34 60° 30° 30°- 60°- 90° Practice 1 2 33 A 2 + B 2 = C 2 A = 2 2 A = 4 A 2 = 3 A =  3 A 2 + B 2 = C 2 A = 2 2 A = 4 A 2 = 3 A =  3

35 30°- 60°- 90° Conclusion: the ratio of the sides in a triangle is  3 Conclusion: the ratio of the sides in a triangle is 33 60° 30° 33 1 2

36 60° 30° 30°- 60°- 90° Practice 4 8 Hypotenuse = short leg * 2 4343 The key is to find the length of the short side. The key is to find the length of the short side. Long Leg = short leg *  3

37 60° 30° 30°- 60°- 90° Practice 5 10 Hypotenuse = short leg * 2 5353 Long Leg = short leg *  3

38 60° 30° 30°- 60°- 90° Practice 7 14 Hypotenuse = short leg * 2 7373 Long Leg = short leg *  3

39 60° 30° 30°- 60°- 90° Practice 33 2323 Hypotenuse = short leg * 2 3 Long Leg = short leg *  3

40 60° 30° 30°- 60°- 90° Practice  10 2  10 Hypotenuse = short leg * 2  30 Long Leg = short leg *  3

41 30°- 60°- 90° Practice

42 60° 30° 30°- 60°- 90° Practice Short Leg = Hypotenuse  2 11  3 Long Leg = short leg *  3

43 60° 30° 30°- 60°- 90° Practice 2 4 Short Leg = Hypotenuse  2 2323 Long Leg = short leg *  3

44 60° 30° 30°- 60°- 90° Practice 9 18 Short Leg = Hypotenuse  2 9393 Long Leg = short leg *  3

45 60° 30° 30°- 60°- 90° Practice Short Leg = Hypotenuse  2 15  3 Long Leg = short leg *  3

46 60° 30° 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2 23  3 Short Leg = Long leg   3

47 60° 30° 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2 14  3 Short Leg = Long leg   3

48 60° 30° 30°- 60°- 90° Practice Hypotenuse = Short Leg * 2 16  3 Short Leg = Long leg   3

49 60° 30° 30°- 60°- 90° Practice 3  3 6363 Hypotenuse = Short Leg * 2 9 Short Leg = Long leg   3

50 60° 30° 30°- 60°- 90° Practice 4  3 8383 Hypotenuse = Short Leg * 2 12 Short Leg = Long leg   3

51 60° 30° 30°- 60°- 90° Practice 9  3 18  3 Hypotenuse = Short Leg * 2 27 Short Leg = Long leg   3

52 60° 30° 30°- 60°- 90° Practice 7  3 14  3 Hypotenuse = Short Leg * 2 21 Short Leg = Long leg   3

53 60° 30° 30°- 60°- 90° Practice 11  3 22  3 Hypotenuse = Short Leg * 2 33 Short Leg = Long leg   3

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