Euclid Geometry Class 9: Introduction To Euclid

In this blog, we will learn about Euclid Geometry of Class 9. A solid has shape, size, and position, and can be moved from one place to another. Its boundaries are called surfaces. They separate one part of the space from another and are said to have no thickness. The boundaries of the surfaces are curved or straight lines. These lines end at points.

Consider the three steps from solids to points. (Solids-surfaces-lines-points). In each step we lose one extension, also called a dimension. So, a solid has three dimensions, a surface has two, a line has one and a point has none. Euclid summarized these statements as definitions.

Euclid Geometry Class 9

A few of them are given below:

A point is that which has no part. By no part means, a point does not occupy any area and space. A line is a breadth-less length. Breadth-less means the width of the line is negligible (insignificant). Because a line has only one dimension, which is the length of the line.

The ends of a line are points. The extremities of lines are points.

A straight line is a line that lies evenly with the points on itself. This means a straight line lies equally with respect to the points on itself. This means a straight line is formed by the collection of points that lies evenly along the straight line.

A surface is that which has length and breadth only. It is clear that the length and breadth account similar to the x and y axes.

The edges of a surface are lines. The surface ABCD has four lines, line AB, BC, CD, and AD.

The last definition states that a plane surface is a surface that lies evenly with the straight lines on itself. To understand this definition, we recall the 4th definition.

A line lies evenly with the points on it; similarly, we can understand that the plane surface is formed by even space lines, which have very close to each other.

Read More: Euclid's Postulates: 5 Postulates - Geometry - Class 9 - Maths