1 / 13

2.1: Triangle Properties

-Triangle Inequalities. 2.1: Triangle Properties. Spingboard activity. GSE’s.

kadeem-byers
Télécharger la présentation

2.1: Triangle Properties

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. -Triangle Inequalities 2.1: Triangle Properties Spingboard activity GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts

  2. Th. 5-9: • If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. 1st identify the sides B Largest angle Largest side: BC 5 Smalles angle Smallest side: AB A 2nd, use the theorem to generalize the angles sizes 11 7 C

  3. Example 1 • In RGY, RG = 14, GY = 12, and RY = 20. List the angles in ascending order.

  4. Example 2 List the angles in descending order 1st- Find the side measures smallest SG= largest SB = BG = middle 2nd- Use the theorem to order the angles Largest, middle, smallest angle

  5. Th. 5-10 • If one angle in a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the smaller angle. B 1st, identify the angles 110 Largest side: AC Largest Angle: 50 C Smallest Angle: Smallest Side BC 2nd, use the theorem to generalize the measures of the sides 20 A

  6. Example List the sides of ABC from Greatest to least

  7. Ex. 2 Find the value of x and list the sides of ROT in order from least to greatest. 7(8)+8 = 64 Ans: 7x+8 + 8x-10 + 7x+6 = 180 22x + 4 = 180 22x = 176 x = 8 8(8) -10 = 54 7(8) + 6 = 62 O 54 RT< RO<TO 62 64 T R

  8. Th. 5.12 Spingboard activity • The sum of the lengths of any two sides of a triangle is greater than the length of the third side

  9. Th. 5.13- SAS inequality • If 2 sides of 1 triangle are congruent to 2 sides of a 2nd triangle, and the included angle of one triangle has a greater measure than the included angle of the 2nd triangle, then the 3rd side of the 1 Triangle is greater than the 3rd side of the 2nd triangle. D Q 80 4 in 4 in 20 6 in 6 in E G F So FE > AG A

  10. Examples

  11. Th. 5.14: SSS Inequality If 2 sides of 1 triangle are congruent to 2 sides of a 2nd triangle and the 3rd side in one triangle is longer than the 3rd side in the 2nd triangle, then the included angle in one triangle is greater than the included angle in the 2nd. I P 5 cm 8 cm 5 cm 8 cm E 12 cm M W 10 cm Q

  12. Examples

  13. Assignments

More Related