Jim Rahn [email protected] Based upon NCTM Triangle ClassificationNCTM Triangle...
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Transcript of Jim Rahn [email protected] Based upon NCTM Triangle ClassificationNCTM Triangle...
![Page 1: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/1.jpg)
Triangle Classification
Jim Rahnwww.jamesrahn.com
Based upon NCTM Triangle Classification
![Page 2: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/2.jpg)
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
![Page 3: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/3.jpg)
A B
All points on the circle whose diameter is AB.
Solution 2
Back to Task 1
![Page 4: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/4.jpg)
A B
All points on the perpendicular to AB at A and B.
Right Triangles
Solution 1
Back to Task 1
Task 2
![Page 5: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/5.jpg)
A B
Task 2: Show all points C, on the plane, where triangle ABC is an isosceles triangle.
Right Triangles
Solution 1
Solution 2
![Page 6: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/6.jpg)
A B
All points on the perpendicular bisector of AB.
Right TrianglesIsosceles Triangles
Back to Task 2
Solution 2
![Page 7: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/7.jpg)
A B
Right TrianglesIsosceles 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
![Page 8: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/8.jpg)
A B
Right TrianglesIsosceles Triangles
Task 3: Find all points C, on the plane, so that triangle ABC is an equilateral triangle.
Solution
![Page 9: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/9.jpg)
A B
Right TrianglesIsosceles TrianglesEquilateral Triangles
All points of intersection of the last two circles.
Task 4
![Page 10: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/10.jpg)
A B
Right TrianglesIsosceles TrianglesEquilateral Triangles
Task 4: Show all points C, on the plane, where triangle ABC is an isosceles right triangle.
Solution 1
Solution 2
![Page 11: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/11.jpg)
A B
4 points on the perpendiculars through A and B so AB=BC and AB=AC
Right TrianglesIsosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Back to Task 4
Solution 2Task 5
![Page 12: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/12.jpg)
A B
2 points on the perpendicular bisector of AB and on the circle through AB.
Right TrianglesIsosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Solution 1
Back to Task 4
Task 5
![Page 13: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/13.jpg)
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
![Page 14: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/14.jpg)
A B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Solution 2
Back to Task 5
Obtuse Triangles
Task 6
![Page 15: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/15.jpg)
A B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Back to Task 5
Solution 1
Task 6
Obtuse Triangles
![Page 16: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/16.jpg)
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.
![Page 17: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/17.jpg)
A B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Task 7
![Page 18: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/18.jpg)
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
![Page 19: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/19.jpg)
A B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
Task 9
![Page 20: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/20.jpg)
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?
![Page 21: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/21.jpg)
A B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
Acute Isosceles Triangle
![Page 22: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/22.jpg)
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
![Page 23: Jim Rahn James.rahn@verizon.net Based upon NCTM Triangle ClassificationNCTM Triangle Classification.](https://reader036.fdocuments.net/reader036/viewer/2022062805/5697bff71a28abf838cbef06/html5/thumbnails/23.jpg)
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.