# Basic Shapes in Geometry

Melissa Bialowas, Yuanxin (Amy) Yang Alcocer
• Author
Melissa Bialowas

Melissa Bialowas has taught preschool through high school for over 20 years. She specializes in math, science, gifted and talented, and special education. She has a Master's Degree in Education from Western Governor's University and a Bachelor's Degree in Sociology from Southern Methodist University. She is a certified teacher in Texas as well as a trainer and mentor throughout the United States.

• Instructor
Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.

Discover what basic geometric shapes are and learn to define and identify them. Learn about two-dimensional and three-dimensional geometric shapes. Updated: 09/26/2021

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## What are the basic Geometric Shapes?

Geometric shapes are closed forms or figures that have lines, angles, and surfaces. Shapes are used throughout life on signs, in art, and in nature. We are familiar with a circular flower, a triangular warning sign, the pyramids, and cubic dice, just to name a few. The root poly means "many," and the root gon means "sides," so a polygon is literally a shape with at least three sides. Two-dimensional (2D) shapes are flat. They have length and width, such as a circle, square, triangle, or rectangle. Three-dimensional (3D) shapes have length, width, and height. These include spheres, circular cylinders, cubes, and rectangular prisms.

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## Two-Dimensional Geometric Shapes

Basic geometric shapes can be seen throughout life. They occur in nature and are recognized around the world. They form the basis of geometry, architecture, and art. Polygons can be as simple as three lines forming a triangle, four lines forming a quadrilateral, or eight lines forming an octagon. They can also be more complex, having hundreds of sides!

### Circle

A circle has one curved line. All points on the line are an equal distance from the center. While a circle is a geometric shape, it is not considered a polygon due to it not having multiple sides.

### Triangle

A triangle has three connected lines and three interior angles. Triangles can be in many configurations. They can have three sides of equal lengths, 2 sides of equal lengths, or no equal length sides.

### Square

A square has four equal sides and four right angles (angles that measure 90 degrees). They are one type of quadrilateral (a shape with four sides), and they are also a type of rectangle.

### Rectangle

A rectangle has two sets of equal sides and four right angles. Thus all squares are rectangles, but not all rectangles are squares. Because it has four sides, a rectangle is another type of quadrilateral.

### Parallelogram

Just as the name has the word parallel in it, the parallelogram has two sets of parallel sides. It has two sets of equal sides, like a rectangle, but it is not required to have right angles. Thus all rectangles and squares are parallelograms, but not all parallelograms are rectangles or squares. A parallelogram is also a quadrilateral.

### Rhombus

A rhombus has four equal sides, but it is not required to have right angles. Therefore, all squares are rhombuses, but not all rhombuses are squares. A rhombus is another common quadrilateral, and because it has two sets of parallel sides, it is also a parallelogram. Some people call this shape a diamond, but that is not a mathematical term.

### Trapezoid

A trapezoid has exactly two parallel sides that have different lengths. They are also considered quadrilaterals.

## Many - Sided Polygons

Polygons can have more than just three or four sides, of course. This is where knowing root words can help in understanding how many sides each figure has.

Shape Root Number of Sides
pentagon  penta  5
hexagon  hexa  6
heptagon  hepta  7
octagon  octa  8
nonagon  nona  9
decagon  deca  10
n-gon    n

After passing ten-sided figures, unique words are no longer used. We would say a polygon with 15 sides is a 15-gon and a polygon with 40 sides is a 40-gon.

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#### What are the basic geometric shapes in art?

In art, lines are used to create an enclosed area. In paintings and photography these are 2D and in many sculptures they are created in 3D. The basic geometric shapes are much the same as in math: circle, square, triangular pyramid, etc.

#### What are basic shapes in mathematics?

Basic shapes are areas closed in by one or more lines. They can be measured in length and width (2D shapes) or length, width, and height (3D shapes).

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