Triangle Classification

Jim Rahnwww.jamesrahn.com

James.rahn@verizon.net

Based upon NCTM Triangle Classification

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

A B

All points on the circle whose diameter is AB.

Solution 2

Back to Task 1

A B

All points on the perpendicular to AB at A and B.

Right Triangles

Solution 1

Back to Task 1

Task 2

A B

Task 2: Show all points C, on the plane, where triangle ABC is an isosceles triangle.

Right Triangles

Solution 1

Solution 2

A B

All points on the perpendicular bisector of AB.

Right TrianglesIsosceles Triangles

Back to Task 2

Solution 2

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

A B

Right TrianglesIsosceles Triangles

Task 3: Find all points C, on the plane, so that triangle ABC is an equilateral triangle.

Solution

A B

Right TrianglesIsosceles TrianglesEquilateral Triangles

All points of intersection of the last two circles.

Task 4

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

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

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

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

A B

Right Triangles

Isosceles Triangles

Isosceles Right Triangles

Equilateral Triangles

Solution 2

Back to Task 5

Obtuse Triangles

Task 6

A B

Right Triangles

Isosceles Triangles

Isosceles Right Triangles

Equilateral Triangles

Back to Task 5

Solution 1

Task 6

Obtuse Triangles

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.

A B

Right Triangles

Isosceles Triangles

Isosceles Right Triangles

Equilateral Triangles

Obtuse Triangles

Acute Triangles

Task 7

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

A B

Right Triangles

Isosceles Triangles

Isosceles Right Triangles

Equilateral Triangles

Obtuse Triangles

Acute Triangles

Obtuse Isosceles Triangles

Task 9

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?

A B

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

Have we covered all the classifications for 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

Try drawing some various triangles using your classifications.