6001 sum of angles polygons

Geometry Drill 1/24/13 Pick up a paper and use your

protractor to find the sum of the interior angles of the polygons that have a check next them.

Write down the sum and the number of sides

Geometry Drill 1/24/13 1. What is the sum of the

angles of a triangle? 2. What is the sum of the

angles of a square?

Objective:

To determine the interior and exterior angle sum in any polygon.

To determine the measure of one interior & one exterior angle of a regular polygon.

POLYGON......1.A CLOSED PLANE FIGURE

2. EACH SEGMENT INTERSECTS EXACTLY TWO OTHER SEGMENTS ONE AT EACH ENDPOINT.

3. MADE OF 3 OR MORE SEGMENTS

WHICH ARE POLYGONS?

Convex or Concave Polygons ?

Convex Polygons

CONVEX POLYGONA polygon in which any line

segment connecting two points has no part outside the polygon.

CONVEX POLYGON.

Sides Interior Angle Sum

3 180

4 360

5 540

6 720

7 900

8 1080

9 1260

10 1440

n

Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is _ .

Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is 180(n–2) _ .

How many exterior angles are in the drawing?

CD

E

exterior angles

E

D C

10 exterior angles

E

D C

We will only be interested in ONE AT A VERTEX

E

D C

Conjecture/ Formula The sum of the measures

of the exterior angles of any convex polygon, one at each vertex is _____.

Conjecture/ Formula The sum of the measures

of the exterior angles of any convex polygon, one at each vertex is 360º.

Regular Polygon

A polygon with all sides and angles congruent.

Conjecture/Formula The measure of one interior

angle of any regular convex polygon is _____.

Conjecture/Formula The measure of one interior

angle of any regular convex polygon is

180(n–2)

n

Conjecture/Formula The measure of one

exterior angle of any regular convex polygon is _____.

Conjecture/Formula The measure of one

exterior angle of any regular convex polygon is 360º

n