1 / 11

7.3 Special Right Triangles

This guide covers the properties of 45°-45°-90° and 30°-60°-90° triangles, known as special right triangles. It explains the theorems regarding side lengths: in a 45°-45°-90° triangle, the hypotenuse is √2 times the length of a leg, while in a 30°-60°-90° triangle, the hypotenuse is twice the shorter leg and the longer leg is √3 times the shorter leg. Numerous examples and exercises are included to reinforce understanding and application of these critical geometric principles.

velika
Télécharger la présentation

7.3 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. 7.3 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. 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.

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

  7. Answer: Your Turn: Find b.

  8. 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

  9. Example 3: Find QR.

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

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

More Related