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Special Right Triangles

Special Right Triangles. Words to Know:. 45 ◦ -45 ◦ -90 ◦ Triangle Theorem. Look. 30 ◦ -60 ◦ -90 ◦ Triangle Theorem. special right Triangles. 45 ◦ -45 ◦ -90 ◦ Special Right Triangles . a 2 + b 2 = c 2. Look!. 45 ◦. 1 2 + 1 2 = y 2. y. 1. x. 1 + 1 = y 2. 45 ◦. 2 = y 2. x. 1.

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Special Right Triangles

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  1. Special Right Triangles

  2. Words to Know: 45◦-45◦-90◦Triangle Theorem Look 30◦-60◦-90◦Triangle Theorem special right Triangles

  3. 45◦-45◦-90◦ Special Right Triangles a2 + b2 = c2 Look! 45◦ 12 + 12 = y2 y 1 x 1 + 1 = y2 45◦ 2 = y2 x 1 2 = y

  4. 45◦-45◦-90◦Triangle Theorem In a 45◦-45◦-90◦ triangle, both legs are congruent, and the length of the hypotenuse is the length of a leg times . 45◦ l l Write 45◦ l

  5. Example #1: Find the value of x. You Try! x 45◦ 17 x =

  6. To find the length of one leg… Know This! If you were given the hypotenuse of a 45-45-90 triangle, to find the length of one of the legs, all you need to do is divide the hypotenuse by 2, then multiply by .

  7. Example #4: Find the value of x. You Try! 20 Check! 45◦ x x=

  8. 45◦-45◦-90◦Triangle Theorem Write! Length of a Leg Hypotenuse 45◦ 3 5 5 4 7 45◦ 18 5 50

  9. Deriving the 30◦-60◦-90◦Triangle Theorem Write! Look! a2 + b2 = c2 60◦ x2 + 12 = 22 30◦ x 2 2 x2 + 1 = 4 x2 = 3 60◦ 60◦ x = 1 2 x =

  10. Deriving the 30◦-60◦-90◦Triangle Theorem Look! a2 + b2 = c2 60◦ x2 + 42 = 82 30◦ x 8 8 x2 + 16 = 64 x2 = 48 60◦ 60◦ x = 4 8 x =

  11. 30◦-60◦-90◦Triangle Theorem Write! The LONGER LEG is times the shorter leg. The HYPOTENUSE is 2 times the shorter leg. 30◦ 2s 60◦ s

  12. 45◦-45◦-90◦Triangle Theorem Makes sense, now…? Write! Length of a Leg Hypotenuse Length of a Leg Hypotenuse 45◦ 6 5 5 9 11 45◦ 16 5

  13. 30◦-60◦-90◦Triangle Theorem Read In a 30◦-60◦-90◦ triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is times the length of the shorter leg. 30◦ 2s 60◦ s

  14. Example #1: Find the value of x and y. You Try! 30◦ 22 x = 11 60◦ x

  15. 30◦-60◦-90◦ Special Right Triangles a (short leg) c (hypotenuse) b (longer leg) 60◦ 1 2 c b 2 4 30◦ 5 10 You Try! a 12 24 20 40 30 60

  16. Find the value of each side. 45o 5 cm 1. You Try! 60o 45o 10 cm 3. 5 cm 30o 2. 4.

  17. 45o 60o cm 45o 30o

  18. Classwork Any Questions…? Oh, yeah! Classwork Rocks!

  19. Objective Objective: • understand and use the properties of special right triangles. • Students know and are able to use angle and side relationships in problems with special right triangles, such as 30◦- 60◦ - 90◦ triangles and 45◦- 45◦ - 90◦ triangles. Look!

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