1. Classify Polygons
Section 1.6

2. Vocabulary
A polygon is a closed two-dimensional shape with straight sides.

3. Vocabulary
A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is called concave.

4. Vocabulary
In an equilateral polygon, all sides are congruent. In an equiangular polygon, all angles in the interior of the polygon are congruent. A regular polygon is a convex polygon that is both equilateral and equiangular.

5. Vocabulary
3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon 11 sides Undecagon 12 sides Dodecagon n sides n-gon

6. EXAMPLE 1
Identify polygons
Tell whether the figure is a polygon and whether it is convex or concave. a. b. c. d.
SOLUTION
Some segments intersect more than two segments, so it is not a polygon. a. b.
The figure is a convex polygon.
Part of the figure is not a segment, so it is not a polygon. c. d.
The figure is a concave polygon.

7. EXAMPLE 2
Classify polygons
Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. a. b.
SOLUTION
The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. a.
The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. b.

8. EXAMPLE 3 Find side lengths
A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side.
ALGEBRA
SOLUTION
First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent.
3x + 6
4x – 2 =
Write equation. 6 =
x – 2
Subtract 3x from each side. 8 = x
Add 2 to each side.

9. Assignment
P. 44: 3-29(odds)