Download 8-1. PINWHEELS AND POLYGONS Inez loves pinwheels. One day

8-1. PINWHEELS AND POLYGONS
Inez loves pinwheels. One day in class, she noticed that if she put three congruent
triangles together so that one set of corresponding angles are adjacent, she could make
a shape that looks like a pinwheel.
a. Can you determine any of the angles of her triangles? Explain how you found
your answer.
b. The overall shape (outline) of Inez’s pinwheel is shown below. How many
sides does it have? What is another name for this shape?
8-2. Inez is very excited. She wants to know if you can build a pinwheel
using any angle of her triangle. Work with your team to build pinwheels and
polygons by placing different corresponding angles together at the center. Create
pinwheels using the Pinwheel 123 Student eTool (GeoGebra).
Alternatively, use both the Pinwheel ABC Student eTool (GeoGebra) and
the Pinwheel DEF Student eTool (GeoGebra). Work together to determine which
congruent triangles can build a pinwheel (or polygon) when corresponding angles are
placed together at the center. For each successful pinwheel, answer the questions
below.

How many triangles did it take to build the pinwheel?

Is the shape familiar? Does it have a name? If so, what is it?
c.
Explain why one triangle may be able to create a pinwheel or polygon while
another triangle cannot.
d.
Jorge has a triangle with angle measures 32°, 40°, and 108°. Will this triangle
be able to form a pinwheel? Explain.

8-4. Jasmine wants to create a pinwheel with equilateral triangles. How many
equilateral triangles will she need? Explain how you know.
.

What is the name for the polygon she created?
8-5. When corresponding angles are placed together, why do some triangles
form convex polygons while others result in non-convex polygons? Consider this as
you answer the following questions.
.
Carlisle wants to build a convex polygon using congruent triangles. He wants
to select one of the triangles below to use. Which triangle(s) will build a convex
polygon if multiple congruent triangles are placed together so that they share a
common vertex and do not overlap? Explain how you know.
a.
For each triangle from part (a) that creates a convex polygon, how many sides
would the polygon have? What name is most appropriate for the polygon?