1. HONORS GEOMETRY 5.3. Inequalities in One Triangle

2. Do Now: Welcome Back! Complete the Do Now given to you when you walked into class today Think or =

3. Reminder: Inequalities involve either: A greater than sign ( > ) OR A less than ( < ) sign

4. Definition of Inequality For any real numbers a and b, a>b if and only if there is a positive number c such that a = b+c. Ex: If 5= 2 + 3 then 5>2 and 5>3

5. Recall: Interior Angles? Exterior Angles? Remote Interior angles? What does the exterior angle theorem claim?

6. So….

7. Exterior Angle Inequality

8. Example One:

9. Example Two:

10. You Try!

11. Triangle Relationship: In a triangle, the smallest angle is opposite the smallest side the largest angle is opposite the largest side

12. Example Three:

13. Example Four:

14. You Try!

15. 2 theorems: 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. If one angle of 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.

16. Example Five:

17. Example Six:

18. You Try!

19. Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me and or your tablemates questions if you are confused.

20. Exit Ticket: