1.6

Warm UpWarm Up

Lesson QuizLesson Quiz

Lesson PresentationLesson Presentation

Classify Polygons

1.6 Warm-Up

1. Draw an acute angle and shade the interior.

2. Find the measure of the supplement of a 130º angle.

ANSWER

ANSWER 50

3. Find the measure of the complement of an 86 angle.

ANSWER 4

1.6 Example 1

SOLUTION

Tell whether the figure is a polygon and whether it is convex or concave.

Some segments intersect more than two segments, so it is not a polygon.

a.

b. The figure is a convex polygon.

d. The figure is a concave polygon.

Part of the figure is not a segment, so it is not a polygon.

c.

b. c.a. d.

1.6 Example 2

SOLUTION

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.a. b.

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.

1.6 Example 2

SOLUTION

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.

c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular.

c.

1.6 Guided Practice

Sketch an example of a convex heptagon and an example of a concave heptagon.

1.

SAMPLE ANSWER

1.6 Guided Practice

Classify the polygon shown at the right by the number of sides. Explain how you know that the sides of the polygon are congruent and that the angles of the polygon are congruent.

2.

Quadrilateral. They all have the same measure; they are all right angles.

ANSWER

1.6 Example 4

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.

Write equation.

Subtract 3x from each side.

Add 2 to each side.

3x + 6 4x – 2=

6 = x – 2

8 = x

1.6 Example 4

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

Then find a side length. Evaluate one of the expressions when x = 8.

303(8) + 6 ==3x + 6

The length of a side of the table is 30 inches.

ANSWER

1.6 Guided Practice

The expressions 8y° and ( 9y – 15 )° represent the measures of two of the angles in the table in Example 3. Find the measure of an angle.

3.

120oANSWER

1.6 Lesson Quiz

1. Draw a convex hexagon.

ANSWER

quadrilaterals ; not regularANSWER

2. This figure shows the tiles on a kitchen floor. What type of polygon are the tiles? Are they regular polygons?

1.6 Lesson Quiz

3. This figure is a regular polygon. Find the length of each side.

ANSWER 16 cm