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Video: Heptagon: Definition, Shapes & Examples



In this lesson, you’ll review the definition of polygons, and you’ll learn what makes heptagons unique. You’ll also distinguish between regular and irregular heptagons.

2016-05-17

 NY Regents Exam – Geometry: Help and Review

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Heptagon: Definition, Shapes & Examples

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Lesson Transcript

Instructor:
Joseph Vigil

In this lesson, you’ll review the definition of polygons, and you’ll learn what makes heptagons unique. You’ll also distinguish between regular and irregular heptagons.

A World of Shapes

In general, a lot of things are called shapes. We have circles, triangles, squares, rectangles…this could go on and on. But only certain shapes are polygons. Polygons are enclosed two-dimensional shapes with straight sides. This definition leaves out circles and ovals because their one side is curved, but that still leaves room for lots of shapes to be polygons.

Heptagons

A heptagon is a seven-sided polygon. It also has seven vertices, or corners where sides meet, and seven angles. The angles are always found at the vertices.

The regular heptagon is probably the most recognizable one:

It’s called a regular heptagon because all sides and angles are congruent. Congruent means they are equal in size and shape.

In this illustration, the vertices are circled. All the angles at these vertices are equal.

Irregular Heptagons

Not all heptagons are regular, however. As previously stated, a heptagon is simply a seven-sided polygon. So heptagons can take on various forms, as long as they’re enclosed and have seven sides.

Here’s an irregular heptagon, or a heptagon whose sides and angles are not congruent:

Even though this heptagon is irregular, it still has seven sides, seven vertices, and seven angles. Here’s the same heptagon with the seven vertices and angles circled:

Here’s another irregular heptagon. It has unequal sides and angles:

irregular heptagon

Don’t forget, though, that a polygon is an enclosed shape. So even if a figure has seven sides, if it’s not enclosed, it’s not a heptagon:

This figure does, indeed, have seven sides, but it’s not enclosed. So, it doesn’t have seven vertices or angles and is not a heptagon.

Lesson Summary

A polygon is an enclosed two-dimensional shape with straight sides. This includes triangles, quadrilaterals, pentagons, etc but not circles or ovals. A heptagon is a seven-sided polygon. Along with seven sides, a heptagon has seven vertices and angles. A regular heptagon is a heptagon that has congruent sides and angles. An irregular heptagon is any heptagon with sides and angles that are not all congruent.


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  • The Parallel Postulate: Definition & Examples

    4:25

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    7:40

  • Parallel Lines: How to Prove Lines Are Parallel

    6:55

  • Using Converse Statements to Prove Lines Are Parallel

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  • What Are Polygons? – Definition and Examples

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    4:15

  • Measuring the Angles of Triangles: 180 Degrees

    5:14

  • How to Measure the Angles of a Polygon & Find the Sum

    6:00

  • What is an Enneagon? – Definition & Formulas

  • Heptagon: Definition, Shapes & Examples

    2:20

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Geometric Shapes

There are several kinds of shapes you will learn in elementary school; this page
will provide you with the names and examples of each one.

Circle

A round shape, drawn like this:

A drawing of a circle

Triangle

A shape with three sides. Sometimes the sides are equal—sometimes they aren’t. Their
names are sometimes different depending on the length of the sides. We will show
you the common ones:

Three kinds of triangles

Equilateral triangle—this triangle has 3 equal sides.

Isosceles triangle—this triangle has 2 equal sides.

Scalene triangle—this triangle has no equal sides.

Square

A box shape, with four equal sides—opposite sides are parallel, drawn like this:

A drawing of a square

Parallel means non-intersecting. For example, parallel lines means that if the two
lines kept going forever, they would never cross over each other—they would always
be an equal distance apart.

Rectangle

Another box shape, with two sets of equal sides. Equal sides are opposite each other.
The sides are parallel to each other. It’s drawn like this:

A drawing of a rectangle

Trapezoid

Another 4 sided shape, with one set of parallel lines (the other set of lines is
not parallel), drawn like this:

A drawing of a trapezoid

Pentagon

A shape with five sides. They can be drawn many different ways, but these are the
most common:

A drawing of two kinds of pentagons

The pentagon on the left is known as a regular pentagon, because all of its sides
are the same length. The one on the right is also a commonly known pentagon, shaped
like a house.

Hexagon

A shape with six sides, drawn like this:

A drawing of a hexagon

Heptagon

A shape with seven sides, drawn like this:

A drawing of a heptagon

Octagon

A shape with eight sides, drawn like this:

A drawing of an octagon

You’ll notice that the octagon is the shape they use for stop signs.

Nonagon

A shape with nine sides, drawn like this:

A drawing of a nonagon

Decagon

A shape with 10 sides, drawn like this:

A drawing of a decagon

Dodecagon

A shape with 12 sides, drawn like this:

A drawing of a dodecagon

Polygons

All of these shapes are polygons. A polygon is a shape made of lines that could
be colored in (all the lines meet and it has a “middle”).

Most of what you will be asked to do with these shapes is recognize them and draw
them, so memorize how many sides they have, what they look like, etc. Other things
may include calculating the area and/or perimeter of these shapes. If you’re trying
to find area or perimeter, read our page on
Area and Perimeter .

<< Prev (Measurement)
Next (Area and Perimeter) >>

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Geometric Shapes

There are several kinds of shapes you will learn in elementary school; this page
will provide you with the names and examples of each one.

Circle

A round shape, drawn like this:

A drawing of a circle

Triangle

A shape with three sides. Sometimes the sides are equal—sometimes they aren’t. Their
names are sometimes different depending on the length of the sides. We will show
you the common ones:

Three kinds of triangles

Equilateral triangle—this triangle has 3 equal sides.

Isosceles triangle—this triangle has 2 equal sides.

Scalene triangle—this triangle has no equal sides.

Square

A box shape, with four equal sides—opposite sides are parallel, drawn like this:

A drawing of a square

Parallel means non-intersecting. For example, parallel lines means that if the two
lines kept going forever, they would never cross over each other—they would always
be an equal distance apart.

Rectangle

Another box shape, with two sets of equal sides. Equal sides are opposite each other.
The sides are parallel to each other. It’s drawn like this:

A drawing of a rectangle

Trapezoid

Another 4 sided shape, with one set of parallel lines (the other set of lines is
not parallel), drawn like this:

A drawing of a trapezoid

Pentagon

A shape with five sides. They can be drawn many different ways, but these are the
most common:

A drawing of two kinds of pentagons

The pentagon on the left is known as a regular pentagon, because all of its sides
are the same length. The one on the right is also a commonly known pentagon, shaped
like a house.

Hexagon

A shape with six sides, drawn like this:

A drawing of a hexagon

Heptagon

A shape with seven sides, drawn like this:

A drawing of a heptagon

Octagon

A shape with eight sides, drawn like this:

A drawing of an octagon

You’ll notice that the octagon is the shape they use for stop signs.

Nonagon

A shape with nine sides, drawn like this:

A drawing of a nonagon

Decagon

A shape with 10 sides, drawn like this:

A drawing of a decagon

Dodecagon

A shape with 12 sides, drawn like this:

A drawing of a dodecagon

Polygons

All of these shapes are polygons. A polygon is a shape made of lines that could
be colored in (all the lines meet and it has a “middle”).

Most of what you will be asked to do with these shapes is recognize them and draw
them, so memorize how many sides they have, what they look like, etc. Other things
may include calculating the area and/or perimeter of these shapes. If you’re trying
to find area or perimeter, read our page on
Area and Perimeter .

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