1. Inequalities in Triangles Angles
Geometry 5-5a

2. Points of Concurrency Type Name Perpendicular Bisectors Circumcenter
Angle Bisectors
Incenter
Medians
Centroid
Altitudes
Orthocenter
Points of Concurrency

3. Points of Concurrency Superpowers
Type
Where
Circumcenter
Equal distance to vertices
Incenter
Equal distance to sides
Centroid
Balancing point
1/3 to side, 2/3 to vertex
Orthocenter
On Euler Line, Nothing special
Points of Concurrency Superpowers

4. Points of Concurrency Where they occur
Type
Where
Circumcenter
Inside Acute
Outside Obtuse
On hypotenuse of Right
Incenter
Inside Triangle
Centroid
Orthocenter
On Right Angle
Points of Concurrency Where they occur

5. Parts of Isosceles Triangle

6. The next page has a visual definition of the word Adjacent
The next page has a visual definition of the word Adjacent. This definition is the same as when the word is used in English class.
What is the English language definition of adjacent?
Definition

7. Triangle Exterior Angles

8. Recall the exterior angle theorem for triangles
Review

9. We can combine inequalities with known equations.

10. How do we combine the comparison property with the exterior angle theorem

11. Investigation 2 - Supplies
Ruler
Protractors
Computer Paper – 1 piece
Investigation 2 - Supplies

12. Everyone Draw a triangle on a blank piece of paper
Investigation 2

13. Use the protractor to measure all the angles in the triangle
Investigation 2

14. Investigation 2 Label the largest angle L Label the smallest angle S
Label the middle sized angle M
Investigation 2

15. Use the ruler to measure the lengths of the three sides
Investigation 2

16. Investigation 2 Label the largest side l Label the smallest side s
Label the middle sized side m
Investigation 2

17. Which side is opposite angle L?
Investigation 2

18. Investigation 2 Which side is opposite angle S?
Is this true for all students?
What conjecture can you make?
Investigation 2

19. What is the converse of this theorem?

20. Theorem

21. Practice

22. Practice

23. Practice

24. Practice

25. Practice

28. Practice

29. Practice

30. Practice

32. Practice

34. Inequalities in Triangles Sides
Geometry 5-5b

35. Triangle Inequalities
What limitations are there on the lengths of triangle sides?
Triangle Inequalities

36. Triangle Inequalities
Here are 21 different triangle with two sides, red and blue the same length
Triangle Inequalities

37. Investigation 1 - Supplies
Spaghetti
Handout – titled “What is the shortest path from A to B”
Investigation 1 - Supplies

38. Investigation How many different triangles CAT could you form?
Break spaghetti pieces to match the lengths on the sheet,
AC, AT, CT
Try to arrange the pieces to make a triangle
How many different triangles CAT could you form?
Investigation

39. You should have been able to form exactly one triangle from the three pieces of spaghetti
Investigation

40. Now break three more pieces to form the sides for the triangle FSH
How many different triangles FSH could you form?
Investigation

41. What must be true about the lengths of the three sides of a triangle in order for the three lengths to form a triangle?
Investigation

42. Theorem

43. Practice

44. Practice

45. Practice

46. Practice

47. Practice

48. Practice

49. Practice

50. Pages 277 – 279
4 – 26 even, 32, 33, 48-55
Homework