Question

for exercises 1 - 3, draw an example of each polygon. 1. quadrilateral 2. dodecagon 3. octagon for exercises 4 - 7, classify each polygon. assume that all sides are straight. for exercises 8 - 10, give one possible name for each polygon. 11. write these definitions using the classify and differentiate method to fill in the blanks. a. an octagon is ____ that __. b. a concave polygon is __ that __. c. a 20 - gon, also called an icosagon, is __ that __. d. an equilateral polygon is __ that ____. 12. name a pair of consecutive angles and a pair of consecutive sides in the figure shown on the right. 13. draw a concave hexagon. how many diagonals does it have?

Explanation:

Step1: Recall polygon definitions

A polygon is a closed - figure with straight sides.

Step2: Answer exercises 1 - 3

1. A quadrilateral is a 4 - sided polygon. For example, a square with 4 equal sides and 4 right angles.
2. A dodecagon is a 12 - sided polygon. One can draw a regular dodecagon with 12 equal sides and 12 equal angles.
3. An octagon is an 8 - sided polygon. A regular octagon can be drawn with 8 equal sides and 8 equal angles.

Step3: Answer exercises 4 - 7

1. The first polygon has 8 sides, so it is an octagon.
2. The second polygon has 6 sides, so it is a hexagon.
3. A circle is not a polygon as it has a curved side.
4. The arrow - shaped figure is not a polygon as it has non - straight parts.

Step4: Answer exercises 8 - 10

1. The polygon has 5 sides, so it is a pentagon.
2. The polygon has 4 sides, so it is a quadrilateral.
3. The polygon has 4 equal sides and 4 right angles, so it is a square.

Step5: Answer exercise 11

a. An octagon is a polygon that has 8 sides.
b. A concave polygon is a polygon that has at least one interior angle greater than 180 degrees.
c. A 20 - gon, also called an icosagon, is a polygon that has 20 sides.
d. An equilateral polygon is a polygon that has all sides of equal length.

Step6: Answer exercise 12

For the given pentagon, a pair of consecutive angles could be ∠A and ∠C, and a pair of consecutive sides could be side AC and side CY.

Step7: Answer exercise 13

To draw a concave hexagon, one can draw a hexagon with one or more "caved - in" parts. The formula for the number of diagonals of an n - sided polygon is $d=\frac{n(n - 3)}{2}$. For a hexagon where n = 6, $d=\frac{6\times(6 - 3)}{2}=\frac{6\times3}{2}=9$.

Answer:

1. Square (example of quadrilateral)
2. Regular dodecagon (example of dodecagon)
3. Regular octagon (example of octagon)
4. Octagon
5. Hexagon
6. Not a polygon
7. Not a polygon
8. Pentagon
9. Quadrilateral
10. Square
11. a. A polygon; has 8 sides

b. A polygon; has at least one interior angle greater than 180 degrees
c. A polygon; has 20 sides
d. A polygon; has all sides of equal length

1. Consecutive angles: ∠A and ∠C; Consecutive sides: AC and CY
2. 9 diagonals