Holt Geometry 6-1 Properties and Attributes of Polygons 6.1 Classify polygons based on their sides...

Holt Geometry

6-1 Properties and Attributes of Polygons

6.1

Classify polygons based on their sides and angles.

Find and use the measures of interior and exterior angles of polygons.

Side of a polygonVertex of a polygonDiagonalRegular polygonConcaveconvex

Polygon Angle Sum TheoremPolygon Exterior Angle Sum Theorem

1.2.3.4.5.6.

Number your paper

Holt Geometry

6-1 Properties and Attributes of Polygons

Classifying polygons by number of sides.

Holt Geometry

6-1 Properties and Attributes of Polygons

A regular polygon is one that is both equilateral and equiangular.

If a polygon is not regular, it is called irregular.

Concave: any diagonal passes outside of the polygon

Convex:no diagonal passes outside the polygon

regular irregular

1.2.3.4.5.

Number your paper

Holt Geometry

6-1 Properties and Attributes of Polygons

Tell whether each polygon is regular or irregular and concave or convex.

1.

2.

3.

4.

5.

Draw these!

Holt Geometry

6-1 Properties and Attributes of Polygons

Examples: Sketch a polygon that meets each of the following characteristics, if possible.

1. convex, irregular hexagon

2. concave triangle.

3. Regular quadrilateral

4. convex nonagon

5. concave, regular pentagon

Holt Geometry

6-1 Properties and Attributes of Polygons

Find the sum of the interior angle measures of each convex polygon by drawing all possible diagonals from one vertex of the polygon.

How does the triangle sum theorem help you?

Holt Geometry

6-1 Properties and Attributes of Polygons

Holt Geometry

6-1 Properties and Attributes of Polygons

Example 1:

Find the sum of the interior angle measures of a convex heptagon.

Holt Geometry

6-1 Properties and Attributes of Polygons

Example 2:

Find the measure of each interior angle of pentagon ABCDE.

Holt Geometry

6-1 Properties and Attributes of Polygons

How would you calculate the measure of each interior angle of a regular decagon?

What if it’s not regular?

Interior Angles Exterior Angles

Sum of all angles

Measure of one if the polygon is REGULAR!

)2(180 n

n

n )2(180

Handbook page 19

Holt Geometry

6-1 Properties and Attributes of Polygons

What is the measure of each interior angle of a regular decagon?

What is the measure of each exterior angle of a regular decagon?

What is the SUM of all of the exterior angles?

Holt Geometry

6-1 Properties and Attributes of Polygons

In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.

Angle measures of a convex polygon with n sides

Interior Angles Exterior Angles

Sum of all angles

Measure of one if the polygon is REGULAR!

)2(180 n

n

n )2(180

360

n

360

Holt Geometry

6-1 Properties and Attributes of Polygons

Find the value of b in polygon FGHJKL.

Example 3:

Holt Geometry

6-1 Properties and Attributes of Polygons

Example 4

Find the measure of each exterior angle of a regular 20-gon.

Holt Geometry

6-1 Properties and Attributes of Polygons

Ann is making paper stars for party decorations. If the pentagon in the center of the star is regular, what is the measure of 1? 2?

2