Lesson 8.4, For use with pages 420-424

Find the value of x.

1. 2.

You need a calculator today!

Lesson 8.4, For use with pages 420-424

ANSWER 30

Find the value of x.

1.

ANSWER 114

2.

You need a calculator today!

8.4 Polygons and Angles

Essential Questions

• Why is it important to be able to identify congruent triangles in everyday life?

• Where in real life can you use the properties of isosceles and equilateral triangles?

• How are the relationships between lines and planes used in the real world?

• What areas in the real world are properties of parallel lines important?

• In this section we will learn how polygons are classified.

• The word poly–gon means many–sided figure. The least number of sides is three. Polygons are “closed” figures, meaning all sides are connected.

• Polygons are many times name by the number of sides. For example TRIANGLE is named “tri” because it has 3 sides.

Polygons can be identified by the number of their sides.

Polygons and Angles8 6.

Polygons A polygon is a closed figure whose sides are line segments that intersect only at their endpoints. In a regular polygon, all the angles have the same measure and all the sides have the same length.

Pentagon Hexagon Heptagon Octagon 12- gon

5 sides 6 sides 7 sides 8 sides 12 sides

Polygons and Angles8 6.

Polygons A polygon is a closed figure whose sides are line segments that intersect only at their endpoints. In a regular polygon, all the angles have the same measure and all the sides have the same length.

Polygons Regular Polygons Not Polygons

Identifying FiguresEXAMPLE 1

Is the figure a polygon, a regular polygon, or not a polygon? Explain.

Polygons and Angles8 6.

Not a polygon. The figure does not have line segments as sides.

Identifying FiguresEXAMPLE 1

Is the figure a polygon, a regular polygon, or not a polygon? Explain.

Polygons and Angles8 4.

Not a polygon. The figure does not have line segments as sides.

Regular polygon. Its angles have equal measures, and its sides have equal lengths.

NOTEBOOK

Sum of all angle measures in an n-gon: (n – 2) • 180º

Angle Measures in a Polygon

Polygons and Angles8 6.

In the activity, you used triangles to find the sum of the angle measures in polygons. In a regular polygon, the measure of one angle is the sum of the angle measures divided by the number of sides.

Measure of one angle in a regular n-gon:(n – 2) • 180º

n

n = number of sides of the polygon

Finding an Angle MeasureEXAMPLE 2

Find the measure of one angle in a regular octagon.

Polygons and Angles8 6.

= 135º

(n – 2) • 180ºn

= (n – 2) • 180ºn

Substitute 8 for n.

Simplify numerator.

Divide.

=1080º

8

ANSWER The measure of one angle in a regular octagon is 135º.

A regular octagon has 8 sides, so use n = 8.8

8

ActivityYou can use triangles to find the sum of the angle measures in other figures.

Look at the table. We will divide each figure into triangles by drawing as many diagonal lines as we can that begin at the point marked.

Shape Quadrilateral Pentagon Hexagon Octagon

Number of Sides

Number of Diagonal Lines

Number of Triangles Formed

Sum of Angle Measures

Polygons and Angles8 6.

5

2

3

540º

6

3

4

720º

8

5

6

1080º

. ...4

1

2

360º

Homework

• Geometric Figures worksheet– Round to the nearest tenth

(one number after the decimal)