Plane Geometry

By the end of this lesson, you will be able to

  • define plane geometry.
  • describe plane and its properties.
  • identify two dimensional shapes.
  • form a plane.
  • analyse geometric dimension.
  • compare plane geometry to solid geometry.

What is Plane Geometry

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.

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

There are two type of elementary geometry in terms of measurement and they are:

  • 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.

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.

Plane Geometric Shapes Example

A rectangle of plane shape is moving around a circle of another plane shape.


With a view to writing if you touch a piece of paper with a pen or pencil, a point is produced. A point is nothing but a position. It does not have any length, breadth or height. That is a point has no part.

Thus, a point has no dimension. Therefore, a point is dimensionless position in geometry.


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!


By arranging a number 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.

Parallel Planes Example

3 parallel planes are in 3 different levels.

Formation of Shapes

point points make line lines make plane L H W planes make solid

A fixed point is seen 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. Solid objects are discussed in solid geometry.

A list of 2-dimensional shapes names

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

Plane Geometric Shapes and Names





A curved line is showing its path A curved line is showing how a curve goes by changing its different directions in different fashion.


Scalene Triangle

Isosceles Triangle

A B C D b a a

Equilateral Triangle

A B C D a a a h

Acute Triangle

70° 60° 50°

Obtuse Triangle

90° < x° < 180°

Right Triangle





trapezium (UK)

trapezoid (US)

Isosceles Trapezoid

isosceles trapezium (UK)

isosceles trapezoid (US)


h b



h b


কোণ ও বাহুর দৈর্ঘ্য নির্দেশক আয়তক্ষেত্র চিত্র কোণ ও বাহু নির্দেশক আয়তক্ষেত্র চিত্র a a b b


a a a a


Regular Polygon






diameter chord radius tangent secant center

Area of Circle

sector segment arc

Conic Section


major-axis center minor-axis latus rectum directrix -a a b -b F1 C P L R F2 M N Q S


axis of symmetry focus latus rectum vertex directrix T F C D A P Q R M N


F1 F2 V1 V2 P C a a