Is it too much to ask for a LITTLE PRECIPITATION?!-Evan

Lesson 4: (3.5) The Polygon Angle-Sum Theorems

LT: To classify polygons and to find the measures of the angles of a polygon.

Classifying Polygons

Polygon: Closed plane figure with at least three sides that are segments intersecting only at their endpoints, and no adjacent sides are collinear.

A

B

C

DE

A

B

C

DE

A

B

C

DE

Not a polygon Not a polygon Polygon

Classifying Polygons

Note: A diagonal of a polygon is a segments that connects two nonconsecutive vertices.

Convex Polygon: A polygon with no diagonal with points outside the polygon

Concave Polygon: A polygon with at least one diagonal with points outside the polygon.

Convex Concave

Classifying Polygons

We can classify polygons according to the number of sides it has.

Sides Name

3

4

5

6

8

9

10

12

n

TriangleQuadrilateral

PentagonHexagonOctagonNonagonDecagon

Dodecagonn-gon

Classifying Polygons

Classify each polygon by its sides. Identify each as convex or concave.

Classifying Polygons

Equilateral Polygon: A polygon with all sides congruent.

Equiangular Polygon: A polygon with all angles congruent.

Regular Polygon: A polygon that is both equilateral and equiangular.

Naming Polygons

CD

G

H

JK

F

Vertices:

Sides:

Angles:

Polygon:

Super Fun Activity!

Sketch polygons with 4, 5, 6, 7, and 8 sides on chart paper Divide into triangles by drawing diagonals from one vertex Multiply the # of Δ’s by 180 to find the polygon angle-sum

# of Sides # of Δ’s Formed

Angle-Sum

4

5

6

7

8

Theorem 3-14: Polygon Angle-Sum Theorem: The sum of the measures of the angles in an n-gon is (n – 2)180.

n

Polygon Angle Sums

Find the sum of the measures of the angles of a regular dodecagon. Then find the measure of an interior angle.

The sum of the angles of a polygon is 720. Find the number of sides the polygon has and classify it.

Polygon Angle Sums

Find x in the following polygon.

125° 125°x°

Polygon Angle Sums

Theorem 3-15: Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

For a pentagon:

m1m2 m3m4 m5 360

1

23

4

5

Polygon Angle Sums

If the measure of an exterior angle of a regular polygon is 30, find the number of sides and classify it.

(3.5) The Polygon Angle-Sum Theorems

It took me like three hours to finish the shading on your upper lip. It's probably the best drawing I've ever done.

-Napoleon

HOMEWORK: (3.5) Pgs. 161-162; #2-26 even, 32, 34, 40,42TERMS: Polygon, Convex Polygon, Concave Polygon,

Equilateral Polygon, Equiangular Polygon, Regular Polygon