Jim Rahn
www.jamesrahn.com
[email protected]
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.
A
B
Solution 1
Solution 2
All points on the circle
whose diameter is AB.
A
B
Back to Task 1
Solution 2
Right Triangles
All points on the
perpendicular to AB at A
and B.
A
B
Solution 1
Back to Task 1
Task 2
Right Triangles
Task 2: Show all points C, on the plane, where triangle ABC is
an isosceles triangle.
A
B
Solution 1
Solution 2
Right Triangles
Isosceles Triangles
All points on the
perpendicular bisector
of AB.
A
B
Back to Task 2
Solution 2
Right Triangles
Isosceles Triangles
A
All points on a circle
with a radius of AB and
a center at B or center
at A
B
Back to Task 2
Solution 1
Task 3
Right Triangles
Isosceles Triangles
Task 3: Find all points C, on the plane, so that triangle ABC is an
equilateral triangle.
A
B
Solution
Right Triangles
Isosceles Triangles
Equilateral Triangles
A
All points of
intersection of the last
two circles.
B
Task 4
Right Triangles
Isosceles Triangles
Equilateral Triangles
Task 4: Show all points C, on the plane, where triangle ABC
is an isosceles right triangle.
A
B
Solution 1
Solution 2
Right Triangles
Isosceles Triangles
Equilateral Triangles
Isosceles Right Triangles
A
4 points on the
perpendiculars
through A and B so
AB=BC and AB=AC
B
Back to Task 4
Solution 2
Task 5
Right Triangles
Isosceles Triangles
Equilateral Triangles
Isosceles Right Triangles
A
2 points on the
perpendicular
bisector of AB and
on the circle
through AB.
B
Back to Task 4
Solution 1
Task 5
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.
A
B
Solution 1
Solution 2
Right Triangles
Isosceles Triangles
Equilateral Triangles
Obtuse Triangles
Isosceles Right Triangles
A
B
Back to Task 5
Solution 2
Task 6
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
A
B
Back to Task 5
Solution 1
Task 6
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Task 6: Find all points C, on the plane, so that acute triangle.
A
B
Solution 1
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
A
B
Task 7
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 isAan obtuse isoscelesBtriangle.
Solution
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
A
B
Task 9
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
B
A
Triangle?
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
Acute Isosceles Triangle
A
B
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
Acute Isosceles Triangle
A
B
Have we covered all the classifications for triangles?
Right Triangles
Isosceles Triangles
Isosceles Right Triangles
Equilateral Triangles
Obtuse Triangles
Acute Triangles
Obtuse Isosceles Triangles
Acute Isosceles Triangle
A
B
Try drawing some various triangles using your
classifications.