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Published bySamara Brewer Modified about 1 year ago

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

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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

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

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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 °

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45°- 45°- 90° = c = c 2 2 = c 2 2 = c = c = c 2 2 = c 2 2 = c ° 22

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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- 22 45°

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

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

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

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45°- 45°- 90° Practice 14 SAME leg* 2 77 77 45°

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45°- 45°- 90° Practice

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3 2 hypotenuse 2 45°

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45°- 45°- 90° Practice 3 2 22 = 3

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45°- 45°- 90° Practice 3 2 hypotenuse 2 45° 3 SAME 3

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45°- 45°- 90° Practice 6 2 hypotenuse 2 45°

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45°- 45°- 90° Practice 6 2 22 = 6

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45°- 45°- 90° Practice 6 2 hypotenuse 2 45° 6 SAME 6

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45°- 45°- 90° Practice 11 2 hypotenuse 2 45°

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45°- 45°- 90° Practice 11 2 22 = 11

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45°- 45°- 90° Practice 11 2 hypotenuse 2 45° 11 SAME 11

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45°- 45°- 90° Practice 8 hypotenuse 2 45°

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45°- 45°- 90° Practice 8 22 22 22 * = 8282 2 = 4 2

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45°- 45°- 90° Practice 8 hypotenuse 2 45° 4242 SAME 4242

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45°- 45°- 90° Practice 4 hypotenuse 2 45°

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45°- 45°- 90° Practice 4 22 22 22 * = 4242 2 = 2 2

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45°- 45°- 90° Practice 4 hypotenuse 2 45° 2222 SAME 2222

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45°- 45°- 90° Practice 6 Hypotenuse 2 45°

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45°- 45°- 90° Practice 6 22 22 22 * = 6262 2 = 3 2

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45°- 45°- 90° Practice 6 hypotenuse 2 45° 3232 SAME 3232

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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 °

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°- 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 °

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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

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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.

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60° 30° 30°- 60°- 90° Practice 1 2 33 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

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30°- 60°- 90° Conclusion: the ratio of the sides in a triangle is 3 Conclusion: the ratio of the sides in a triangle is 33 60° 30° 33 1 2

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60° 30° 30°- 60°- 90° Practice 4 8 Hypotenuse = short leg * 2 4343 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

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60° 30° 30°- 60°- 90° Practice 5 10 Hypotenuse = short leg * 2 5353 Long Leg = short leg * 3

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60° 30° 30°- 60°- 90° Practice 7 14 Hypotenuse = short leg * 2 7373 Long Leg = short leg * 3

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60° 30° 30°- 60°- 90° Practice 33 2323 Hypotenuse = short leg * 2 3 Long Leg = short leg * 3

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

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30°- 60°- 90° Practice

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

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60° 30° 30°- 60°- 90° Practice 2 4 Short Leg = Hypotenuse 2 2323 Long Leg = short leg * 3

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60° 30° 30°- 60°- 90° Practice 9 18 Short Leg = Hypotenuse 2 9393 Long Leg = short leg * 3

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

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

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

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

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60° 30° 30°- 60°- 90° Practice 3 3 6363 Hypotenuse = Short Leg * 2 9 Short Leg = Long leg 3

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60° 30° 30°- 60°- 90° Practice 4 3 8383 Hypotenuse = Short Leg * 2 12 Short Leg = Long leg 3

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

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

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

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