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Euclid Geometry

 

Euclid was a Greek mathematician who studied planes and solid figures by applying various theorems and axioms. He introduced the concept of plane surfaces and flat figures in his famous book, Elements.

The term geometry is coined from the Greek word - geo and metrein. The word geo means earth, and metrein means to measure. Geometry deals with all the lines, angles, shapes, points, etc., present all over the globe. Euclid used universal facts and figures to postulate the theorems and axioms. He also found relationships between all things on earth and dealt with their properties.

Euclid termed congruence of triangles, the similarity of triangles, areas, Pythagoras theorem, circles, regular polygons, and conic sections under volume and regular solids.

Properties of Euclidean geometry

  1. It deals with the study of solid geometry and plane geometry.
  2. It gives a proper definition of a line, point, and plane.
  3. According to Euclidean geometry, a solid has a definite shape, size, and position. A solid can be moved from one place to another.
  4. The interior angles of a triangle are a sum of 180 degrees.
  5. Two parallel lines never cross each other.
  6. The shortest distance between two points is always a straight line.

Seven axioms of Euclidean geometry

  1. Things which are equal to the same thing are equal.
  2. If equals are added to equals, the wholes are equal.
  3. If equals are subtracted from equals, the remainder are equal.
  4. Things which coincide with one another are equal.
  5. The whole is greater than the part.
  6. Things which are double of the same things are equal.
  7. Things which are halves of the same things are equal.

Postulates of Euclid

Euclid postulated some statements in his book Elements. Before proceeding with his postulates, let us have a look at these statements-

  1. Assume the three steps from solids to points as solids-surface-lines-points. In each step, one dimension is lost.
  2. A solid has three dimensions, the surface has 2, the line has one, and the point is dimensionless.
  3. A point is anything with no part; a breadthless length is a line and the ends of a line point.
  4. A surface is something that has length and breadth only.

Postulate 1: - A straight line can be drawn from one point to another point.
Postulate 2: - A terminated line can be further produced indefinitely.
Postulate 3: - A circle can be drawn with any center and any radius.
Postulate 4: - All right angles are equal.
Postulate 5: - If a straight line falling on two other 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 the side on which the sum of angles is less than two right angles.

Geometric Worksheet of Euclid

  1. How many dimensions do solids, points, and surfaces have?
  2. What is the shape of a pyramid’s base?
  3. If a + b =10 and a = c, then prove that c + b =10.
  4. Can two distinct intersecting lines be parallel to each other at the same time? Justify.
  5. Read the following sentence and mention which of Euclid’s axioms is followed: “X’s salary is equal to Y’s salary. Due to the recession, the salaries of X and Y are reduced to half. Now the final salary of X will still be equal to Y.”

Can you find the answers to these questions? Leaving over to you!

NCERT Class 9 Maths Chapter 5 is solely dedicated to Euclid's Geometry, it gives students an introduction to geometry and its applications.

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