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Special Right Triangles

Special Right Triangles. 45° 45° 90° and 30° 60° 90°. 45°. Y. X. 45°. X. Z. The legs are congruent because sides opposite congruent angles are congruent. Legs are congruent. Hypotenuse = leg times the √2. hypotenuse. leg. leg. Y. 12ft. 8in. X. 45°. 45°. X. Y. X= 6√2 ft.

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Special Right Triangles

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  1. Special Right Triangles 45° 45° 90° and 30° 60° 90°

  2. 45° Y X 45° X Z The legs are congruent because sides opposite congruent angles are congruent

  3. Legs are congruent Hypotenuse = leg times the √2 hypotenuse leg leg

  4. Y 12ft 8in X 45° 45° X Y X= 6√2 ft X= 8in Y= 6√2 ft Y= 8√2 in

  5. 2X 2X Y X 2X The two right triangles are congruent so Z=2X 60° Z Z 60° 60° Z

  6. Hypotenuse = 2 short legs Long leg = short leg • 3 Hypotenuse Long Leg 60° Short Leg

  7. Y 16 X Y 60° 60° 7 X 16=2X X = 7√3 Y = 14 X = 8 Y = 8√3

  8. Y Y 5√3 9 60° 60° X X 5√3=X√3 X = 3√3 Y = 6√3 X = 5 Y = 10

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