1 / 18

Special Right Triangles

Special Right Triangles. Objectives. Use properties of 45 ° - 45° - 90° triangles Use properties of 30° - 60° - 90° triangles. Side Lengths of Special Right ∆s.

dante
Download Presentation

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. Objectives • Use properties of 45° - 45° - 90° triangles • Use properties of 30° - 60° - 90° triangles

  3. Side Lengths of Special Right ∆s • Right triangles whose angle measures are 45° - 45° - 90°or 30° - 60° - 90°are called special right triangles. The theorems that describe the relationships between the side lengths of each of these special right triangles are as follows:

  4. 45° - 45° - 90°∆ Theorem 7.6 In a 45°- 45°- 90° triangle, the length of the hypotenuse is √2 times the length of a leg. hypotenuse = √2 • leg x√2 45 ° 45 °

  5. Example 1: WALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°- 45°- 90° triangle measures millimeters?

  6. The length of the hypotenuse of one 45°- 45°- 90° triangle is millimeters. The length of the hypotenuse is times as long as a leg. So, the length of each leg is 7 millimeters. The area of one of these triangles is or 24.5 millimeters. Example 1: Answer: Since there are 8 of these triangles in one square quadrant, the area of one of these squares is 8(24.5) or 196 mm2.

  7. WALLPAPER TILING If each 45°- 45°- 90° triangle in the figure has a hypotenuse of millimeters, what is the perimeter of the entire square? Your Turn: Answer: 80 mm

  8. The length of the hypotenuse of a 45°- 45°- 90° triangle is times as long as a leg of the triangle. Example 2: Find a.

  9. Divide each side by Answer: Example 2: Rationalize the denominator. Multiply. Divide.

  10. Answer: Your Turn: Find b.

  11. 30° - 60° - 90°∆ Be sure you realize the shorter leg is opposite the 30°& the longer leg is opposite the 60°. Theorem 7.7 • In a 30°- 60°- 90° triangle, the length of the hypotenuse is twice as long as the shorter leg, and the length of the longer leg is √3 times as long as the shorter leg. 60 ° 30 ° x√3 Hypotenuse = 2 ∙ shorter legLonger leg = √3 ∙ shorter leg

  12. Example 3: Find QR.

  13. is the longer leg, is the shorter leg, and is the hypotenuse. Answer: Example 3: Multiply each side by 2.

  14. Your Turn: Find BC. Answer: BC = 8 in.

  15. COORDINATE GEOMETRY is a30°-60°-90° triangle with right angle X and as the longer leg. Graph points X(-2, 7) and Y(-7, 7), and locate point W in Quadrant III. Example 4:

  16. Graph X and Y. lies on a horizontal gridline of the coordinate plane. Since will be perpendicular to it lies on a vertical gridline. Find the length of Example 4:

  17. is the shorter leg. is the longer leg. So, Use XY to find WX. Point W has the same x-coordinate as X.W is located units below X. Answer: The coordinates of W are or about Example 4:

  18. COORDINATE GEOMETRY is at 30°-60°-90° triangle with right angle R and as the longer leg. Graph points T(3, 3) and R(3, 6) and locate point S in Quadrant III. Answer: The coordinates of S are or about Your Turn:

More Related