1 / 15

Special Right Triangles - Hypotenuse and Leg Relationships

Learn how to find the hypotenuse and leg lengths in special right triangles, including 45-45-90, equilateral, and 30-60-90 triangles. Discover the relationships between the sides and angles using multiplication, division, and square root operations.

ralkire
Download Presentation

Special Right Triangles - Hypotenuse and Leg Relationships

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. 7.3 Special Right Triangles Chapter 7 Area

  2. Find the Hypotenuse, leave your answer in simplest radical form. 4 3 3 4 2 What do you notice? 2

  3. 45-45-90 Triangles (Isosceles Right Triangles) • The Legs are congruent • The Hypotenuse is the leg • times the √2 x√2 x x

  4. 45-45-90 Triangles (Isosceles Right Triangles) 5 5

  5. 45-45-90 Triangles If you are given the hypotenuse and Must find the leg, DIVIDE by √2 10√2

  6. 45-45-90 Triangles If you are given the hypotenuse and Must find the leg, DIVIDE by √2 20

  7. To Recap: 45-45-90 Triangles • Leg to Hypotenuse: Multiply by √2 • Hypotenuse to Leg: Divide by √2 • The Legs are always Congruent x√2 x x

  8. Equilateral Triangles • In an Equilateral Triangle, all sides and angles are congruent. Therefore, each angle is 60°. 60° 60° 60°

  9. Equilateral Triangles • If we cut it in half, what happens? Using Pythagorean Theorem, solve for the height of the triangle in simplest radical form. 30° 30° 10 10 5√3 60° 60° 5

  10. 30-60-90 Triangles • Long Leg is across from the 60° angle • Short Leg is across from the 30° angle • Hypotenuse is across from the right angle 30° Hypotenuse Long Leg 60° Short Leg

  11. 30-60-90 Triangles • Short Leg is always your starting point • Long Leg is √3 times the Short Leg • Hypotenuse is 2 times the Short Leg 30° Hypotenuse 2x Long Leg x√3 60° Short Leg x

  12. 30-60-90 Triangles • Short Leg to Hypotenuse: Multiply by 2 • Hypotenuse to Short Leg: Divide by 2 • Short Leg to Long Leg: Multiply by √3 • Long Leg to Short Leg: Divide by √3 30° Hypotenuse 2x Long Leg x√3 60° Short Leg x

  13. 30-60-90 Triangles 4 30° 60° 12 30° 60°

  14. 30-60-90 Triangles 30° 60° 6√3 15

  15. Practice

More Related