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

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.

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.

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°

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

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.

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

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

Then, draw an example of a heptagon.

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.

3 triangles 120° 1 1 1

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

9 triangles 40°

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

18 triangles 20°

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

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.

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

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

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

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°

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

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.

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

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

convex concave

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.

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.

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

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

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

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

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

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