Course 1

8-7 Polygons8-7 Polygons

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Course 1

8-7 Polygons

Warm UpTrue or false?

1. Some trapezoids are parallelograms.

2. Some figures with 4 right angles are squares.

3. Some quadrilaterals have only one right angle.

false

true

true

Course 1

8-7 Polygons

Problem of the Day

Four square tables pushed together can seat either 8 or 10 people. How many people could 12 square tables pushed together seat?

14, 16, or 26 people

Course 1

8-7 Polygons

Learn to identify regular and not regular polygons and to find the angle measures of regular polygons.

Course 1

8-7 Polygons

Vocabulary

polygonregular polygon

Course 1

8-7 Polygons

Triangles and quadrilaterals are examples of polygons. A polygon is a closed plane figure formed by three or more line segments. A regular polygon is a polygon in which all sides are congruent and all angles are congruent.

Polygons are named by the number of their sides and angles.

Course 1

8-7 Polygons

An equilateral triangle has three congruent sides.Remember!

Course 1

8-7 Polygons

Additional Example 1A: Identifying Polygons

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

The shape is a closed plane figure formed by 3 or more line segments.polygon

There are 5 sides and 5 angles.pentagon

All 5 sides do not appear to be congruent.not regular

Course 1

8-7 Polygons

Additional Example 1B: Identifying Polygons

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

There are 8 sides and 8 angles.octagon

The sides and angles appear to be congruent.regular

The shape is a closed plane figure formed by 3 or more line segments.

polygon

Course 1

8-7 Polygons

Check It Out: Example 1A

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

There are 4 sides and 4 angles.

quadrilateral

The sides and angles appear to be congruent.

regular

Course 1

8-7 Polygons

Check It Out: Example 1B

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

There are 4 sides and 4 angles.

quadrilateral

All 4 sides do not appear to be congruent.

not regular

Course 1

8-7 Polygons

The sum of the interior angle measures in a triangle is 180°, so the sum of the interior angle measures in a quadrilateral is 360°.

Course 1

8-7 Polygons

Additional Example 2: Problem Solving Application

Malcolm designed a wall hanging that was a regular 9-sided polygon (called a nonagon). What is the measure of each angle of the nonagon?

11 Understand the Problem

The answer will be the measure of each angle in a nonagon.

List the important information:

• A regular nonagon has 9 congruent sides and t 9 congruent angles.

Course 1

8-7 Polygons

22 Make a Plan

Make a table to look for a pattern using regular polygons.

Solve33Draw some regular polygons and divide each into triangles.

Additional Example 2 Continued

Course 1

8-7 Polygons

720°

The prefixes in the names of the polygons tell you how many sides and angles there are.

tri- = three quad- = four

penta- = five hexa- = six octa- = eight

Reading Math

Additional Example 2 Continued

Course 1

8-7 Polygons

The number of triangles is always 2 fewer than the number of sides.

A nonagon can be divided into 9 – 2 = 7 triangles.

The sum of the interior angle measures in a nonagon is 7 180° = 1,260°.

So the measure of each angle is 1,260° ÷ 9 = 140°.

Solve Cont.33

Additional Example 2 Continued

Course 1

8-7 Polygons

Look Back44

Each angle in a nonagon is obtuse. 140° is a reasonable answer, because an obtuse angle is between 90° and 180°.

Additional Example 2 Continued

Course 1

8-7 Polygons

Check It Out: Example 2

Sara designed a picture that was a regular 6-sided polygon (called a hexagon). What is the measure of each angle of the hexagon?

11 Understand the Problem

The answer will be the measure of each angle in a hexagon.

List the important information:

• A regular hexagon has 6 congruent sides and 6 congruent angles.

Course 1

8-7 Polygons

22 Make a Plan

Make a table to look for a pattern using regular polygons.

Solve33Draw some regular polygons and divide each into triangles.

Check It Out: Example 2 Continued

Course 1

8-7 Polygons

The number of triangles is always 2 fewer than the number of sides. A hexagon can be divided into 6 – 2 = 4 triangles.

The sum of the interior angles in a octagon is 4 180° = 720°.

So the measure of each angle is 720° ÷ 6 = 120°.

Check It Out: Example 2 Continued

Solve Cont.33

Course 1

8-7 Polygons

Look Back44

Each angle in a hexagon is obtuse. 120° is a reasonable answer, because an obtuse angle is between 90° and 180°.

Check It Out: Example 2 Continued

Course 1

8-7 Polygons

Lesson Quiz

1. Name each polygon and tell whether it appears to be regular or not regular.

2. What is the measure of each angle in a regular

dodecagon (12-sided figure)?

150°

nonagon, regular; octagon, not regular