8-7 Polygons Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

8-7 Polygons

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes

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

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

8-7 Polygons

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

8-7 Polygons

Vocabulary

polygonregular polygondiagonal

8-7 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.

8-7 Polygons

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

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

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

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

8-7 Polygons

You can divide any quadrilateral into two triangles by drawing a diagonal, a line segment that connects two non-adjacent vertices. 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°.

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.

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

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

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

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

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.

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

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

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

8-7 Polygons

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

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

8-7 Polygons

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

A. pentagon, not regular

B. hexagon, regular

C. heptagon, regular

D. octagon, not regular

Lesson Quiz for Student Response Systems

octagon, not regular octagon, not regular

8-7 Polygons

2. What is the measure of each angle in a regular decagon (10-sided figure)?

A. 108

B. 144

C. 150

D. 140

Lesson Quiz for Student Response Systems

octagon, not regular octagon, not regular