Sculpting
The hierarchy of triangles:
Polygon
Triangle
Scalene
Isosceles
Equilateral
Definitions of Classifications of Triangles:
Triangle-a closed shape that has 3 sides and 3 angles
Right triangle-a triangle with one right (90 degree) angle
Obtuse triangle-a triangle with one obtuse (more than 90 degree) angle
Acute triangle-a triangle with one acute (less than 90 degree) angle
Scalene-a triangle that has all sides different lengths
Equilateral-a triangle that has all side lengths the same
Isosceles-a triangle that has two side lengths the same
Your Task:
Susan was in charge of designing a sculpture for the courtyard in front of the movie theater. She is supposed to
compose the sculpture of only triangles. So, she will create a sketch of her sculpture. She decided that before she tried
to design her sculpture, she’d better figure out what types of triangles there were and what they were composed of.
She cut out a bunch of triangles that she found on the internet.
Your task is to help Susan categorize her triangles into the groups you were given the definitions for. You may
write on the triangles if you wish to. Create a representation to show what you have found on your blank paper.
Susan found out a lot about triangles after she explored their properties. She found the hierarchy that you see
at the top of the paper. She wants to figure out why the hierarchy is the way that it is. With your triangles, come up
with a defense that you could share with others for why the hierarchy works the way it does. Write it down somewhere
on your blank paper.
On your graph paper, you need to sketch a design for your own sculpture. It can look like anything you want.
However, the company who is buying your sculpture for the courtyard has a few conditions for you: You must use only
triangles, just like Susan had to. At least three of your triangles must have a vertex that is a plotted point, labeled as
ordered pairs on the paper. Your sculpture must have at least one set of parallel lines and at least two sets of
perpendicular ones. At least two of your triangles must be isosceles and at least one must be right. You must have at
least one equilateral triangle. You need to label all of these conditions on your sketch so that the company can see that
you met all of their requirements.
Do you see any part/parts of your sculpture that supports the hierarchy? Which ones? Write about how you
can prove that they support the hierarchy.