1. How Can Build It? Pg. 19 Pinwheels and Polygons
2.6
How Can Build It?
Pg. 19
Pinwheels and Polygons

2. 2.6 – How Can I Build It?______________
Pinwheels and Polygons
In this section you will discover the names of the many different polygons and how they are classified.

3. 2.30 – PINWHEELS AND POLYGONS
Itzel loves pinwheels. One day in class, she noticed that if she put three congruent triangles together, that one set of the corresponding angles are adjacent, she could make a shape that looks like a pinwheel.

4. a. Can you determine any of the angles of her triangles
a. Can you determine any of the angles of her triangles? Explain how you found your answer.
360 3
120°
120°
120°

5. b. The overall shape (outline) of Itzel's pinwheel is shown at right
b. The overall shape (outline) of Itzel's pinwheel is shown at right. How many sides does it have? What is another name for this shape? 1
6 sides 2
hexagon 6
120°
120°
120° 3 4 5

6. c. Itzel's shape is an example of a polygon because it is a closed, two dimensional figure made of straight line segments connected end-to-end. As you study polygons in this course, it is useful to use these names because they identify how many sides a particular polygon has. Some of these words may be familiar, while others may be new. Fill in the names of the polygons below. Then, draw an example of a heptagon.

7. triangle quadrilateral pentagon hexagon heptagon
Name of Polygon
# of sides 3 4 5 6 7
triangle
quadrilateral
pentagon
hexagon
heptagon

8. octagon nonagon decagon dodecagon n – gon
Name of Polygon
# of sides 8 9 10 12 n
octagon
nonagon
decagon
dodecagon
n – gon

9. Then, draw an example of a heptagon.

10. 2.31 – MAKING PINWHEELS
Itzel is very excited. She wants to know if you can build a pinwheel using any angle of her triangle. Obtain a set of triangles from your teacher. Work with your team to build pinwheels and polygons by placing different corresponding angles together at the center. You will need to use the triangles from all four team members together to build one shape. Be ready to share your results with the class.

12. 3 triangles
120° 1 1 1

13. Measure of the central angle
# of triangles needed
Measure of the central angle 1 2 3 3
120°

14. 9 triangles
40°

15. Measure of the central angle
# of triangles needed
Measure of the central angle 1 2 3 3
120° 9
40°

16. 18 triangles
20°

17. Measure of the central angle
# of triangles needed
Measure of the central angle 1 2 3 3
120° 9
40° 18
20°

18. 2.32 –PINWHEEL PATTERNS
Jorge likes Itzel's pinwheels but wonders, "Will all triangles build a pinwheel or a polygon?”
a. Use the different triangles provided by your teacher. Work together to determine which congruent triangles can build a pinwheel (or polygon) when corresponding angles are placed together at the center. If it works, fill in the table.

19. Measure of the central angle
# of triangles needed
Measure of the central angle A B C D E F
45° 8
Not possible 5
72°
Not possible 12
30°
Not possible

20. It must divide by 360° evenly
b. Explain why one triangle may be able to create a pinwheel or polygon while another triangle cannot.
It must divide by 360° evenly

21. Yes, the 40° divides in evenly
c. Jorge has a triangle with interior angle measures 32°, 40°, and 108°. Will this triangle be able to form a pinwheel? Explain? If so, at what angle?
Yes, the 40° divides in evenly

22. 2.33 –POLYGONS
Jasmine wants to create a pinwheel with equilateral triangles.
a. How many equilateral triangles will she need? Explain how you know.
60°
360 60
60°
60° 6
60°
60°
60°

23. hexagon b. What is the name for the polygon she created? 60° 60° 60°

24. c. Jasmine's shape is an example of a convex polygon, while Inez's shape, shown at right is non-convex (or concave). Study the examples below and write a definition of a convex polygon on your paper.

25. All vertices point outward
Has vertices going inward, like a cave

26. convex concave 2.34 –CONCAVE VS. CONVEX
Brenda noticed that the non-convex (concave) shapes all had a part that went inward, like a cave. She decided to investigate more. Sort the shapes below as either "convex" or "concave".
convex
concave

27. convex
concave

28. 2.35 –EQULATERAL, EQUIANGLUAR, AND REGULAR
Brenda was curious about the relationship between the sides and angles of polygons. When all sides are equal, it is called equilateral. When all angles are equal, the polygon is called equiangular. When it has all equal sides AND all equal angles it is called regular.

29. Classify the name of the polygon by the number of sides
Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Then determine if it is convex or concave.

30. hexagon Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave

31. pentagon Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave

32. octagon Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave

33. decagon Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave

34. heptagon Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave

35. quadrilateral Name: _______________ Equilateral, Equiangular, Regular
Convex OR Concave