Geometry

We are not only learning the geometry but also playing with geometry from our childhood. It involves all shapes, their properties, solids, perimeter, area, volume, surface area of solid surfaces and shapes, coordinate system and all theorems based on it.

The mainly geometry can be studied in two parts, plane geometry and solid geometry.

Before going to learn about plane and solid geometry we see some basic shapes of geometry.

  • Point, line, plane and solid are the basics shapes of geometry.
  • A point is having no dimension and it has only its position.
  • Line is the one dimensional shape which is locus of points along straight path.
  • Plane is the two dimensional shape having two coordinates.
  • Finally, solid means a three dimensional shapes which is having 3 coordinates.

Now we see in detailed about plane geometry and solid geometry.

We can represents point, line and plane in two dimensional coordinate system. While solid can be represented in three dimensional coordinate system only.

1) Plane geometry:

  • Plane geometry involves the shapes or objects which are two dimensional.
  • The two dimensional shapes are square, rectangle, triangle, circle etc.
  • Also, it includes perimeter, area of these shapes also.
  • We can locate the two dimensional shapes in two dimensional coordinate system in XY-plane.
  • We can define or locate all two dimensional shapes in XY-plane.
  • Plane geometry involves types of lines, types of angles, types of triangles and their properties.
  • The shapes in two dimensions has only sides, perimeter and area.
  • Polygon and their types also involves in plane geometry.
  • Two dimensional object does not possess faces and edges, they have only sides and vertices.

2) Solid geometry:

  • Solid geometry involves all the three dimensional shapes like cube, sphere, cylinder, cone, prism etc. with their properties such as surface area, volume etc.
  • Two locate three dimensional shapes in geometry we use three dimensional coordinate system i.e. in XYZ- coordinate system.
  • Solid geometry involves all the three dimensional shapes and their properties also.
  • Two dimensional objects are located in two dimensional coordinate system.
  • Three dimensional objects have faces, edges and vertices also.

Two dimensional coordinate system:

  • In two dimensional coordinate system, we can locate two dimensional shapes withe each point on them in two coordinate form.
  • It includes XY-plane with 4 quadrant.
  • In first quadrant, x and y both are positive.
  • In second quadrant x is negative and y is positive.
  • In third quadrant, x and y both are negative.
  • And in fourth quadrant, X is positive and y is negative.
  • The following figure shows the two dimensional coordinate system in which a line is located with the points on it.
  • In this way, we can represent any two dimensional object in XY-plane.
  • The two dimensional geometric figure like circle, ellipse, hyperbola, curves, straight lines, quadratic equations, different types of charts are explained with the help of XY-coordinate system.
  • The x and y coordinates are the intercepts made by the object on that axis respectively.

Fig. Two dimensional Coordinate system (Cartesian coordinate system)

Three dimensional coordinate system:

  • It is used for geometric representation of three dimensional shapes like cube, sphere, cylinder, cone etc.
  • We can study the three dimensional shapes and their properties with the help of three dimensional coordinate system.
  • In this system all the three axes X, Y and Z are mutually perpendicular to each other as shown in figure.
  • In three dimensional coordinate system we can represent any object by three coordinates as (x, y, z).
  • The perpendicular drawn from object or shape to particular coordinate axis gives the value of the coordinate of that axis.

Fig. Three dimensional coordinate system


Updated: July 22, 2021 — 9:29 pm

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