1 / 19

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.

amal
Télécharger la présentation

Special Right Triangles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related