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Triangles and Lines – Special Right Triangles There are two special right triangles :

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle. Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle

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Triangles and Lines – Special Right Triangles There are two special right triangles :

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  1. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle

  2. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg 30 2x 60 x

  3. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x 60 x

  4. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x =10 Example # 1 : Find the other two sides if the hypotenuse = 10 60 x

  5. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x =10 Example # 1 : Find the other two sides if the hypotenuse = 10 60 x = 5

  6. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x =10 Example # 1 : Find the other two sides if the hypotenuse = 10 60 x = 5

  7. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x Example # 2 : Find the other two sides if the shortest side = 8 60 x = 8

  8. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x =16 Example # 2 : Find the other two sides if the shortest side = 8 60 x = 8

  9. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x =16 Example # 2 : Find the other two sides if the shortest side = 8 60 x = 8

  10. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x Example # 2 : Find the other two sides if the medium length side = 60 x

  11. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x Example # 2 : Find the other two sides if the medium length side = 60 x = 13

  12. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 30 2x = 26 Example # 2 : Find the other two sides if the medium length side = 60 x = 13

  13. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem… 45 ? 1 45 B C 1

  14. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem… 45 1 45 B C 1

  15. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 45 x 45 B C x

  16. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 45 Example # 1 : Find the hypotenuse if the congruent sides = 6 6 45 B C 6

  17. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 45 Example # 1 : Find the hypotenuse if the congruent sides = 6 6 45 B C 6

  18. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 45 Example # 2 : Find the congruent sides if the hypotenuse = x 45 B C x

  19. Triangles and Lines – Special Right Triangles There aretwo special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle A The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 45 Example # 2 : Find the congruent sides if the hypotenuse = 15 45 B C 15

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