Triangle Classification

1. Jim Rahn www.jamesrahn.com James.rahn@verizon.net Triangle Classification Based upon NCTM Triangle Classification

2. Line segment AB is placed on the plane. Task 1: Show all point C, on the plane, where triangle ABC is a right triangle. B A Solution 1 Solution 2

3. All points on the circle whose diameter is AB. B A Back to Task 1 Solution 2

4. Right Triangles All points on the perpendicular to AB at A and B. B A Solution 1 Back to Task 1 Task 2

5. Right Triangles Task 2: Show all points C, on the plane, where triangle ABC is an isosceles triangle. B A Solution 1 Solution 2

6. Right Triangles All points on the perpendicular bisector of AB. Isosceles Triangles B A Back to Task 2 Solution 2

7. Right Triangles Isosceles Triangles B A All points on a circle with a radius of AB and a center at B or center at A Back to Task 2 Solution 1 Task 3

8. Right Triangles Isosceles Triangles Task 3: Find all points C, on the plane, so that triangle ABC is an equilateral triangle. B A Solution

9. Right Triangles Isosceles Triangles Equilateral Triangles B A All points of intersection of the last two circles. Task 4

10. Right Triangles Isosceles Triangles Equilateral Triangles Task 4: Show all points C, on the plane, where triangle ABC is an isosceles right triangle. B A Solution 1 Solution 2

11. Right Triangles Isosceles Triangles Equilateral Triangles Isosceles Right Triangles B A 4 points on the perpendiculars through A and B so AB=BC and AB=AC Back to Task 4 Solution 2 Task 5

12. Right Triangles Isosceles Triangles Equilateral Triangles Isosceles Right Triangles B A 2 points on the perpendicular bisector of AB and on the circle through AB. Back to Task 4 Solution 1 Task 5

13. Right Triangles Isosceles Triangles Equilateral Triangles Isosceles Right Triangles Task 5: Find all points C, on the plane, where triangle ABC is an obtuse triangle. B A Solution 1 Solution 2

14. Right Triangles Isosceles Triangles Equilateral Triangles Obtuse Triangles Isosceles Right Triangles B A Back to Task 5 Solution 2 Task 6

15. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles B A Back to Task 5 Solution 1 Task 6

16. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Task 6: Find all points C, on the plane, so that acute triangle. B A Solution 1

17. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles B A Task 7

18. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Task 7: Where are the points C that form a triangle ABC that is an obtuse isosceles triangle. B A Solution

19. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Obtuse Isosceles Triangles B A Task 9

20. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Obtuse Isosceles Triangles Task 9: Where are the points C that produce an Acute Isosceles Triangle? B A

21. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Obtuse Isosceles Triangles Acute Isosceles Triangle B A

22. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Obtuse Isosceles Triangles Acute Isosceles Triangle B A Have we covered all the classifications for triangles?

23. Right Triangles Isosceles Triangles Isosceles Right Triangles Equilateral Triangles Obtuse Triangles Acute Triangles Obtuse Isosceles Triangles Acute Isosceles Triangle B A Try drawing some various triangles using your classifications.