exploring polygons. what are polygons? a polygon is a closed figure made by joining line segments,...

Exploring Polygons

What are polygons?

A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.

The following are examples of polygons:

The figures below are not polygons. Can you tell why?

Regular Polygons

A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.

The following are examples of regular polygons:

Would a square be a regular polygon? A rectangle?

The following are not examples of regular polygons:

How do you know?

TrianglesAll three-sided polygons.

There are many special types of triangles.

QuadrilateralA four-sided polygon.

Angles in quadrilaterals…Quadrilaterals have four sides and four angles.

The sum of the measures of the angles is 360°.

Find the value of x in the quadrilateral below

x° + 105° + 80° + 95° = 360°

Add 105°, 80°, and 95°.

x° + 280° = 360°

THINK: What measure

added to 280° equals 360°?

80° + 280° = 360°

x° = 80°

Find the value of x in each quadrilateral.

A rectangle has opposite sides congruent and parallel, and all right

angles.

Are rectangles a kind of quadrilateral?

How do you know?

A square has all sides congruent, opposite sides parallel, and all right

angles.

Are squares a kind of rectangle?

How do you know?

A parallelogram has opposite sides congruent and parallel, and opposite

angles congruent.

Are parallelograms a kind of rectangle? How do you know?

A rhombus has all sides congruent, opposite sides parallel, and opposite

angles congruent.

How are rhombuses and squares similar? How are rhombuses and squares different?

A trapezoid has exactly one pair of opposite sides parallel.

There are special types of trapezoids ….that’s for another day!

Classify each quadrilateral.

PentagonA five-sided polygon

a regular pentagon

an irregular pentagon

HexagonA six-sided polygon.

a regular hexagon

an irregular hexagon

HeptagonA seven-sided polygon

A regular heptagon

an irregular heptagon

OctagonAn eight-sided polygon.

A regular octagon

An irregular octagon

NonagonA nine-sided polygon.

A regular nonagon

An irregular nonagon

DecagonA ten-sided polygon.

A regular decagon

An irregular decagon