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Introduction to Euclid's Geometry CLASS 9

Euclid's Geometry



Class 9 maths NCERT chapter 5 Introduction to Euclid's Geometry will help students to understand the basic geometry concepts and their applications.

The word geometry originated from the Greek word ‘Geo’ means earth and ‘Metrein’ means to measure. Geometry is ancient branch of mathematics Which studied by various civilizations at different times. Euclid's geometry deals with the study of solids and planes based on the axioms and postulates given by the Egyptian mathematician Euclid.

It mainly deals with points, lines, circles, curves, angles, planes, solids, etc.

In this topic,we shall study the origin of geometry and its link to present-day geometry.Euclid's axioms and postulates are still studied today for a better understanding of geometry.

Some Important definitions suggested by Euclid

  • A line is a breathless length.
  • A point has no dimension.
  • A line which lies evenly with the points on itself is a straight line.
  • Points are the ends of a line.
  • A surface is that which has breadth and length only.
  • A plane surface is a surface which lies evenly with straight lines on itself.

Euclid’s axioms

Euclid’s axioms were :

  • Things which are equal to the same thing are equal to one another.
  • If equals are added to equals, the wholes are equal.
  • If equals are subtracted from equals, the remainders are equal.
  • Things which coincide with one another are equal to one another.
  • The whole is greater than the part.
  • Things which are double the same things are equal to one another.
  • Things which are halves of the same things are equal to one another.
  • Lines are the edges of a surface.

Euclid’s Postulates

There were five postulates given by Euclid

  • Postulate 1:

    A straight line can be drawn from any one point to any other point.

  • Postulate 2:

    A terminated line can be produced indefinitely.

  • Postulate 3:

    A circle can be drawn with any centre and any radius.

  • Postulate 4:

    All right angles are equal to one another.

  • Postulate 5:

    If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
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