1 / 15

Special Cases, for Right Triangles 30° 60° 90° Triangles

Special Cases, for Right Triangles 30° 60° 90° Triangles. 60°. 30 °. 45°. 45° 45° 90° Triangles. 45°. 1. 1. 1. An equilateral triangle is also equiangular , all angles are the same . 60°. 2.

abedi
Download Presentation

Special Cases, for Right Triangles 30° 60° 90° 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 Cases, for Right Triangles 30° 60° 90° Triangles 60° 30° 45° 45° 45° 90° Triangles 45°

  2. 1 1 1. Anequilateraltriangleisalsoequiangular, allangles are thesame. 60° 2 2. Let’sdrawanAltitudefromone of thevertices. Whichisalso a Median and Angle bisector. 30° 60° 2 30° 3. Thebisectedsideisdividedintotwoequalsegments and thebisectedangle has nowtwo 30° equalangles. 2 60° Congratulations! Two 30° 60° 90° triangleshavejustbeenborn Oooh …and youwatched!!!!

  3. Let’s separate the top triangle and label the unknown side as z. 2 2 1 30° 30° 1 2 2 2 2 = z + 1 2 2 4 = z + 1 2 3 = z 2 3 = z z = 3 60° 60° 60° apply the Pythagorean Theorem to find the unknown side. 1 1 30° 30° -1 -1 z = 3 z When, the smallest side is equal to 1, the hypotenuse is 2 times as big, 1 * 2 = 2 And the other leg is times as big, 1 * = Can we generalize this result for all 30°-60°-90° right triangles?

  4. 60° 2 1 30° 3 3 2 60° 1 (.5) 30° (.5) 3 (.5) 60° (2) 2 4 2 (2) 1 Yes itworks! 30° (2) Isthis true for a trianglethatistwice as big? Isthis true for a trianglethatishalfthe original size? Yes , itstillworks. Ifweknow 1 sidelength of a 30-60-90 triangle, we can use thispatterntofindtheother 2 sides

  5. s s 3 3 s 60° 2 30° In a 30°-60°-90° triangle, thehypotenuseistwice as long as theshorterleg, and thelongerlegis times as long as theshorterleg.

  6. 3 3 3 y = x y = 2 60° 2 s s 30° s Find the values of the variables. Round your answers to the nearest hundredth. y 2x = 14 30° 2x = 14 x 2 2 14 60° x =2 Is this 30°-60°-90°? 90°-30°=60° Then we know that:

  7. Find the values of the variables. Round your answers to the nearest unit. 2 ( ) = y = y 90 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 = x y= 60 90 30 90 30 60 30 90 = x 90 = x ( ) 2 y =104 = x 60° 3 2 s = x s x= 30° x = 52 s 2x = y 30° y 90 . OR 60° = x x Isthis a 30°-60°-90°? 90°-60°=30° OR

  8. Find the values of the variables. Find the exact answer. 2 ( ) = y = y 30 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 = x y= 10 30 30 20 20 10 10 30 = x 30 = x ( ) 2 = x 60° 3 2 s = x s x= 30° s x 2x = y 60° y . 30 30° = x Is this a 30°-60°-90°? 90°-60°=30°

  9. 1 1 1 1 Let’sdraw a diagonal forthesquare. The diagonal bisectstherightangles of thesquare. Whatkind of righttriangles are formed?

  10. 1 45° 45° 45° 1 1 1 45° 45° 45° 1 1 2 2 2 y = 1 + 1 2 y = 1 + 1 2 y = 2 2 y = 2 y = 2 y The triangles are 45°-45°-90° Let’s draw the bottom triangle and label the hypotenuse as y Let’s apply the Pythagorean Theorem to find the hypotenuse.

  11. 45-45-90 Right Triangle x x Can we generalize our findings?

  12. 2 2 In a 45°-45°-90° triangle, thehypotenuseis times as long as a leg And bothlegs are thesamesize. 45° s s 45° s

  13. Find the values of the variables. Round your answers to the nearest tenth. 36 2 2 2 2 2 2 2 2 2 2 2 2 2 2 = x 18 18 18 36 36 36 = x 36 = x ( ) 2 y = 25.5 = x 2 45° s = x s x = y = 45° x = 25.5 s 45° 36 x . If y = x then 45° OR = x y Is this a 45°-45°-90°? 90°-45°=45° OR

  14. Find the values of the variables. Give an exact answer. 42 2 2 2 2 2 2 2 2 2 2 2 2 2 2 = x 42 21 21 21 42 42 = x 42 = x ( ) 2 = x 2 45° s = x s x = y = 45° s 45° 42 x . If y = x then 45° = x y Is this a 45°-45°-90°? 90°-45°=45°

  15. 2 2 2 21 x 45° s s y = y= 45° s Find the values of the variables. Give the exact answer. x = 21 45° y x 45° 21 Is this a 45°-45°-90°? 90°-45°=45°

More Related