Polygons: Definitions, Parts, and Classifications

These question-and-answer flashcards cover the definition, parts, and various classifications of polygons, including regularity, side counts, angle measures, and convex versus concave properties.

What is the definition of a polygon?

A closed plane figure made up of three or more straight line segments that do not cross.

What are the line segments that form a polygon called?

Sides.

What is the common endpoint of two sides of a polygon called?

Vertex.

Besides sides and vertices, what other two elements are parts of a polygon?

Angles and diagonals.

What is a diagonal in a polygon?

A segment that connects two nonconsecutive vertices.

How is an interior angle of a polygon defined?

An angle formed between two adjacent sides inside the polygon.

What is an exterior angle of a polygon?

The angle between any side of a polygon and its extended adjacent side.

How many sides does a triangle have, and what is its interior angle measure in a regular polygon?

3 sides; each interior angle measures 60°.

How many sides does a quadrilateral have, and what is its interior angle measure in a regular polygon?

4 sides; each interior angle measures 90°.

How many sides does a pentagon have, and what is its interior angle measure in a regular polygon?

5 sides; each interior angle measures 108°.

How many sides does a hexagon have, and what is its interior angle measure in a regular polygon?

6 sides; each interior angle measures 120°.

Provide the number of sides and regular interior angle for a heptagon.

7 sides; each interior angle measures approximately 128.571°.

How many sides does an octagon have, and what is its regular interior angle measure?

8 sides; each interior angle measures 135°.

State the number of sides and regular interior angle for a nonagon.

9 sides; each interior angle measures 140°.

Give the number of sides and regular interior angle for a decagon.

10 sides; each interior angle measures 144°.

What is the name of an 11-sided polygon and its regular interior angle measure?

Hendecagon (or Undecagon); each interior angle measures about 147.273°.

How do you refer to a polygon with n sides?

An n-gon.

What is the formula for the sum of interior angles of an n-gon?

Sum = (n − 2) × 180°.

When is a polygon called a regular polygon?

When all its sides and all its angles are equal.

What is an irregular polygon?

A polygon whose side lengths or angle measures are not all equal.

What is an equilateral polygon?

A polygon whose sides are all equal in length.

What is an equiangular polygon?

A polygon whose interior angles are all equal in measure.

Define a convex polygon.

A polygon with all interior angles less than 180°, where any line drawn through the polygon intersects it at most twice.

Define a concave polygon.

A polygon that has one or more interior angles greater than 180°, causing a line drawn through it to intersect the polygon more than twice.

If a polygon has 15 sides, what is it called?

A 15-gon.