Geometry Segment 1 Notes

Topics: Polygon, Regular polygon, Angle Pages: 3 (517 words) Published: July 3, 2013
Geometry Segment 1 Notes . POLYGONS

All of the figures you saw in the slideshow were polygons. A polygon is a closed figure with three or more sides. The prefix poly- means “many” while -gon means “angle.” So a polygon is a many-angled figure.

5 Sides : Pentagon

6 Sides : Hexagon

7 Sides : Heptagon

8 Sides : Octagon

9 Sides : Nonagon

10 Sides : Decagon

11 Sides : Hendecagon

12 Sides : Dodecagon

A regular polygon is a many-sided figure where the sides are all equal in length and the angles have the same degree. So what would make a polygon irregular? If any of the sides is shorter or longer than another side or if one or more angles are different, then the polygon is an irregular polygon.

A convex object is one that curves outward, such as the picture frame shown. Therefore, a convex polygon is a many-sided figure where each vertex points away from the center.

A more formal definition states that any segment with endpoints contained in the interior of the polygon must be entirely contained within the polygon to be considered convex. Every regular polygon is convex.

A concave object is one that curves inward, such as the satellite dish shown. Consequently, a concave polygon must be a polygon where one or more vertex points toward the center.

A more formal definition states that a concave polygon has at least one segment where the endpoints are contained in the interior of the polygon but parts of the segment pass outside the polygon.

You may also distinguish between a concave and convex polygon by looking at the angle measures of the interior angles. All interior angles of a convex polygon are less than 180°. In a concave polygon, at least one interior angle will measure more than 180°. Most of the polygons you will investigate in this lesson will be convex polygons.

Lesson six .01

An interior angle is an angle on the inside of a figure. You know a triangle's...