Geometry Lesson Plan - Basics of Euclidean Geometry

Euclid wrote a book named “Elements”. The book is considered as the Bible for Euclidian geometry. In the book he discusses plane geometry, solid geometry and the number theory. In order to systematize the geometrical knowledge, Euclid describes five postulates and five “common notions". These postulates and common notions are called the basics of Euclidian’s geometry.

The five postulates or axioms are the fundamental properties of geometry. There are no formal proofs for the postulates and one postulate cannot be derived from the other:

• By joining any two points one can draw a straight line segment.
• Upon infinitely extending, a straight line segment will remain a straight line.
• A straight line segment can be used as a radius for drawing a circle using one of its end points as a centre.
• All right angles are equal.
• If two straight lines intersect another straight line in such a manner that the summation of the internal angles created by the two straight lines to the third line is less than two right angles then the first two lines will intersect each other upon extending.

Apart from the five postulates, Euclid discusses five “common notions” in his book. Again these are the fundamental truths of geometry and number theory:

• If two or more things are equal to another common thing then the first set of things are equal to each other.
• If two or more things are equal to each other then, by equally adding to all the things will not disturb the equality. For example, if A and B are equal to each other and if C is added to both A as well as B, then the sum A+C and B+C will remain equal.
• If two or more things are equal to each other then equally subtracting to all will not disturb the equality. For example, if A and B are equal to each other and if C is subtracted from both A as well as B, then the sum B-C and A-C will remain equal.
• If one thing is coinciding to another then both of them are equal.
• The part is always less than the whole.

• Talk about Euclid and his book “Elements”
• Tell all the postulates and common notions among the students.
• You can use notations like A, B or simple figures to explain it properly.
• Draw three lines on the board for describing the five postulates.

The basics of Euclidian geometry are the fundamentals of geometry.