section 1.6. in geometry, a figure that lies in a plane is called a plane figure. a polygon is a...

Section 1.6

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Section 1.6

In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties.

Identifying Polygons

Page 3: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Properties of Polygons

Page 4: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

1. It is formed by three or more line segments called sides.

2. Each side intersects exactly two sides, one at each endpoint, so that not two sides with a common endpoint are collinear.

Each endpoint of a side is a vertex of the polygon.

The plural of a vertex is vertices.

A polygon can be named by listing the vertices in consecutive order.

For example, ABCDE and CDEAB are

both correct for the polygon at the right.

Page 5: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon.

A polygon that is not convex is called nonconvex or concave.

Page 6: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Tell whether the figure is a polygon. If it is not, explain why not. If it is a polygon, tell whether it is convex or concave.

It is not a polygon, since some segments intersect more than two segments.

Example 1

Page 7: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Is a polygon and it is convex.

It is a polygon and it is concave.

Page 8: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

A polygon is named by the number of sides.

Classifying Polygons

Page 9: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Number of Sides Type of Polygon3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon9 Nonagon

10 Decagon12 Dodecagonn n-gon

Page 10: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

The term n-gon, where n is the number of a polygon sides, can also be used to name a polygon.

For example, a polygon with 14 sides is a 14-gon.

Page 11: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

In an equilateral polygon, all sides are congruent.

In an equiangular polygon, all angles are congruent.

A regular polygon is a convex polygon that is both equilateral and equiangular.

Page 12: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular.

The polygon is an octagon.

It is a regular polygon.

Example 2

Page 13: Section 1.6. In geometry, a figure that lies in a plane is called a plane figure. A polygon is a closed plane figure with the following properties. Identifying

Given an equilateral hexagon. Find the length of each side.

4x + 3 = 5x – 1

x = 4

side = 4(4) + 3 = 19 mm

Example 3

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