Geometric shapes are foundational elements in both mathematics and daily life. Understanding geometric shapes helps learners describe and interpret the world around them with precision. This reference is designed to teach essential vocabulary about geometric shapes to English learners.

Contents

## Types of Geometric Shapes: 2D Geometric Shapes

By definition, geometric shapes are the purest form of an object or figure in the sense that no matter how much it is moved, rotated, enlarged, or reflected in the mirror, it will just stay in the same form as it was originally when you still did not touch it. To put it in even simpler terms, if you say that something is a circle in geometry, no matter what angle you look at it or how much you fiddle around with it, it will still have the property of a geometric circle.

With the birth of geometry, mathematicians started to make rules on what makes a certain geometric shape and these rules defined the different types of geometric shapes that we have today.

Geometric Shapes – Created by 7ESL

To make it simpler, geometric shapes are divided into two major groups depending on their dimensions. The first group consists of two-dimensional (2D) shapes, which have length and width while the second group consists of three-dimensional (3D) shapes that have length, width, and depth.

As explained above, 2D geometric shapes have length and width. Under 2D shapes, there are two further classifications namely polygons and non-polygons. Polygons are two-dimensional geometric shapes that are made up of straight lines that meet up at one of their endpoints and forms a closed figure. Non-polygons on the other hand, are closed figures made up of curved lines or a combination of straight lines and curved lines.

**1. Triangles**

A triangle is a type of polygon that exactly has three sides and three vertices, or corners. There are different kinds of triangles and they are classified through the length of their sides or through their interior angles.

*Types of triangles according to the lengths of sides*

**A. Equilateral Triangle**

It is a kind of triangle with all three sides having the same length.

**B. Isosceles Triangle**

It is a kind of triangle that exactly has two sides of equal length.

**C. Scalene Triangle**

It is a kind of triangle that has no sides of equal length.

*Types of triangles according to interior angles*

**A. Right Triangle**

A triangle that has a 90-degree interior angle. The side directly opposite of this angle is called the hypotenuse, which is also the longest side of a right triangle.

**B. Oblique Triangle**

It is simply a triangle that does not have a 90-degree interior angle. Under oblique triangles are two more types namely:

**B.1. Acute Triangle**

These triangles all have three of their interior angles measuring less than 90 degrees.

**B.2. Obtuse Triangle**

These triangles have one interior angle which measures above 90 degrees.

**C. Degenerate Triangle**

It is a triangle that has an interior angle of 180 degrees. However, it technically looks like a line segment if you try to draw it.

**2. Quadrilaterals**

Quadrilaterals are polygons that have exactly four sides and four corners. Quadrilaterals are divided into two major types namely, simple and complex.

**A. Simple Quadrilateral**

Simple quadrilaterals are quadrilaterals that do not intersect in themselves. This type is further divided into two which are:

**A.1. Convex Quadrilaterals**Â – All quadrilaterals belonging to this type does not have an interior angle of more than 180 degrees. The following are its types:

**A1.1. Trapezium**

A quadrilateral that has no sides that are parallel with each other.

**A1.2. Trapezoid**

A quadrilateral that has exactly one pair of parallel sides.

**A1.3. Isosceles Trapezoid**

A trapezoid that has base angles of equal value.

**A1.4. Parallelogram**

A quadrilateral with two pairs of parallel sides.

**A1.5. Rhombus**

A quadrilateral with four equal sides.

**A1.6. Square**

A type of rhombus which has four right angles.

**A1.7. Rectangle**

A type of parallelogram with all interior angles measuring 90 degrees.

**A1.8. Kite **

A quadrilateral that has adjacent sides of equal lengths.

**A.2. Concave Quadrilaterals**

A quadrilateral with an interior angle greater than 180 degrees. It only has one type which is called dart.

**B. Complex Quadrilateral**

These quadrilaterals intersect in themselves which makes it look like a simple bow-tie in shape.

**3. Concave and Convex Polygons**

The main difference between concave and convex polygons lies in the measurement of their interior angles. A convex polygon simply has all of its interior angles measuring less than 180 degrees while a concave polygon has one or more interior angles going beyond 180 degrees.

**3.1. Convex Polygon**

**3.2. Concave Polygon**

**4. Regular and Irregular Polygons**

These two are other classifications of a polygon wherein regular polygons both have sides of equal lengths and interior angles of equal measurement. The most common examples of a regular polygon include an equilateral triangle, a square, a pentagon, and hexagons, and octagons. Irregular polygons, on the other hand, are figures which do not satisfy both conditions to be considered as a regular polygon.

**4.1. Regular Polygons**

**4.2. Irregular Polygons**

**5. Curve 2D shapes**

As the name suggests, curved 2D shapes are closed figures formed by purely curved lines or a combination of straight lines and curved lines. As discussed earlier, all curved 2D shapes are also considered non-polygons. The most common examples of such geometric shapes are circles, ellipses, arcs, sectors, segments, parabolas, and hyperbolas.

**5.1. Circle**

**5.2. Ellipse**

**5.3. Sectors**

**5.4. Parabola**

**5.5. Hyperbola**

## Types of Geometric Shapes: 3D Geometric Shapes

As mentioned earlier, three-dimensional (3D) shapes also known as solid figures, are figures that have both length, width, and an additional dimension which is termed as depth. Mathematically speaking, there are a lot of solid figures but the main types are as follows:

**1. Cuboid**

This type of solid figure has six faces in the shape of a rectangle. Each adjacent side of its face meets up and form an exact 90-degree angle.

**2. Parallelepiped**

This figure is just like a cuboid except that its faces are parallelograms instead of rectangles. Hence, its adjacent faces do not create 90-degree angles.

**3. Rhombohedron**

This figure is a parallelepiped with all of its edges having the same length.

**4. Polyhedron **

These are any solid figures which have polygonal faces that are flat as well as having sharp corners and straight edges.

**5. Prism**

These are solid figures which have two bases that have identical dimensions connected by identical faces that are strictly parallelograms. The number of faces corresponds to the number of sides that the bases have.

**6. Cone**

A solid figure with a circular base that smoothly tapers to a point which is called a vertex.

**7. Cylinder**

A cylinder is a solid figure with two circular bases at the top and bottom. Its sides are parallel with each other and its cross-section could be a circle or an oval depending on how it is cut.

**8. Ellipsoid **

This figure is made by rotating an ellipse on its own axes.

**9. Lemon**

This figure is made by rotating a circular arc on its major axis.

**10. Hyperboloid**

This solid figure is created when a hyperbola is rotated in one of its principal axes.

**11. Platonic Solids**

These solids are regular, convex polyhedrons made up of faces that are regular polygons each. In geometry, only five solid figures have met these criteria and they are as follows:

**11.1. Tetrahedron**

Four faces

**11.2. Cube**

Six faces

**11.3. Octahedron**

Eight faces

**11.4. Dodecahedron**

Twelve faces

**11.5. Icosahedron**

Twenty faces

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