1 / 9

Inequalities in One Triangle

Inequalities in One Triangle. Geometry CP1 (Holt 5-5) K. Santos. Theorem 5-5-1. If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Y X Z ( In a triangle, larger angle opposite longer side )

fatima-ortega
Download Presentation

Inequalities in One Triangle

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. Inequalities in One Triangle Geometry CP1 (Holt 5-5) K. Santos

  2. Theorem 5-5-1 If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. Y X Z (In a triangle, larger angle opposite longer side) If XZ > XY then m<Y> m<Z

  3. Example List the angles from largest to smallest. A 10 B 5 8 C Largest angle: <C <A Smallest angle: <B

  4. Theorem 5-5-2 If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle. A B C (In a triangle, longer side is opposite larger angle) If m<A>m<B then BC>AC

  5. Example List the sides from largest to smallest. A 5060 B C Find the missing angle first: 180 – (50 +60) m < C = 70 Largest side: Smallest side:

  6. Triangle Inequality Theorem (5-5-3) The sum of the lengths of any two sides of a triangle is greater than the length of the third side. X Y Z XY + YZ> XZ YZ + ZX >YX ZX + XY>ZY add two smallest sides together first

  7. Examples: Can you make a triangle with the following lengths? • 4, 3, 6 4 + 3 > 6 add the two smallest numbers 7 > 6 triangle • 3, 7, 2 3 + 2 > 7 5 > 7 not a triangle • 5, 3, 2 3 + 2 > 5 5 >5 not a triangle

  8. Example: The lengths of two sides of a triangle are given as 5 and 8. Find the length of the third side. 8 – 5 = 3 5 + 8 = 13 The third side is between 3 and 13 3 < s < 13 where s is the missing side

  9. Example: Use the lengths: a, b, c, d, and e and rank the sides from largest to smallest. d 59 Hint: find missing angles aec 61 5960 b In the left triangle: e > b > a In the right triangle: c > d > e But notice side e is in both inequality statements. So, by using substitution property you can write one big inequality statement. c > d > e> b > a

More Related