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ay!!

11.1-Polygon Basicspolygon

“poly” = many…and “gon” = sides

So a polygon is a closed shape with 3 or more sides.

Examples:

Triangle Rectangle Hexagon

11.1-Polygon BasicsEvery polygon has the

same features: Sides – at least 3 sides made of straight line segments

Vertices (aka endpoints) – connects the sides and forms <s

Angles – at least 3 <s with varying degrees (each less than 180°)

11.1-Polygon Basics# of Sides Type of Polygon Pic of Polygon

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

12 Dodecagon

n n-gon

11.1-Polygon BasicsSpecial Terms for Polygons:

Convex – no line of a side contains a point inside the polygon

Concave (aka nonconvex) – line of a side contains a point inside the polygon

Regular Polygon – convex polygon that is both equilateral and equiangular

Consecutive Vertices – endpoints that are on same side (back-to-back)

Diagonal – segment that joins 2 nonconsecutive vertices

11.1-Polygon BasicsInterior Angles Theorem

The sum of the interior angles of a convex n-gon is:

(n-2) * 180°Example:

Find the sum of the angles in the figure:

Octagon

11.1-Polygon BasicsExample:

Find the value of x in the figure:

Quadrilateral108

°

x°

121°

59°

11.1-Polygon BasicsExample:

The sum of the measures of the interior angles of a convex polygon is 900°. Classify the

polygon by the number of sides.

11.1-Polygon BasicsExterior Angles Theorem

The sum of the exterior angles of a convex n-gon is:

m<1 + m<2 + … + m<n = 360°

Example:Find the value of x in the figure below:

86°

90°

3x

x