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Plane Geometry

Plane geometry is a part of geometry deals with two dimensional space.

You will have learned what is a plane in geometry.

This tutorial will teach you how a is formed from the origin.

You will be introduced to all 2d shapes.

Plane Geometry is the geometry of two dimensional geometric shapes.

Plane geometry is also called Euclidean plane geometry.

So, it refers to the geometry of plane shapes.

The study of geometry is generally divided into two types:

  • Plane geometry
  • Solid geometry

Plane geometry is related to two-dimensions whereas solid geometry deals with 3-dimensions. Plane geometry deals with flat objects. So, all plane shapes exist on flat surface. Lines, triangles, circles, ellipses, for examples, all are flat shapes can be drawn on a piece of flat paper.

An algebraic rule, (x+y)² = x²+2xy+y², is derived from plane shape.

What is a plane in geometry

To understand plane geometry, one has to have a clear concept of plane

Again, a clear concept of point and line is prerequisite of studying plane.

Well. Let's go.


With a view to writing if you touch a piece of paper with a pen or pencil, a point is produced.

It has no length or width.

Thus, a point has no dimension.


A line is the set of points that extends along a straight path infinitely on and on its opposite direction.

It has only length.

So, a line has one dimension.

Now, pay a close attention!


If you arrange a set of lines one after another, it produces a plane.

A plane is all about two dimensional flat surface that expands infinitely.

The two dimensions are length and width.

The length and width must lie in the same plane.

Thus, a plane has two dimensions.

All 2d shapes lie in the plane.

Three parallel planes are shown in the figure.

Three parallel planes are in 3 different levels.

Formation of Shapes

Point Points make Line Lines make Plane L H W Planes make Solid

You can see a fixed point in the first figure.

A set of points makes a line in the second figure.

In the third figure, a set of lines obtained from the second figure makes a plane.

And lastly, six planes make a solid.

We will cover solid geometry in another tutorial.

A list of 2d shapes names given below.

  • Point
  • Line
  • Curve
  • Scalene Triangle
  • Isosceles Triangle
  • Equilateral Triangle
  • Acute Triangle
  • Obtuse Triangle
  • Right Triangle
  • Irregular Quadrilateral
  • Trapezium/Trapezoid
  • Isosceles Trapezium
  • Parallelogram
  • Kite
  • Rhombus
  • Rectangle
  • Square
  • Regular Polygon
  • Pentagon
  • Hexagon
  • Octagon
  • Circle
  • Ellipse
  • Parabola
  • Hyperbola

All two dimensional figures above can be drawn on a piece of paper or on a plane.

Plane Geometry Example


An Ellipse

Yes, we are seeing an ellipse.

A list of 2d shapes names and 2d shape properties are given below.

Plane Geometry


Irregular Quadrilateral (UK)

Trapezium (US)


Trapezium (UK)

Trapezoid (US)

Isosceles Trapezoid

Isosceles Trapezium (UK)

Isosceles Trapezoid (US)

Last revised this page (day/month/year): 28/12/17