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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

18. A B 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. Solution

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

20. A B 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?

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

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

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