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Triangle Classification

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

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Triangle Classification

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  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.

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