Euclidean geometry is the study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid. In its rough outline, Euclidean geometry is the plane and solid geometry commonly taught in secondary schools. For details
class 9 maths chapter 5 solutions can be referred to.
Euclid’s axioms· Things which are equal to the same thing are also equal to one another. · If equals be added to equals, the wholes are equal. · If equals be 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. |
Euclid’s Postulates
- To draw a straight line from any point to any point.
- To produce a finite straight line continuously in a straight line.
- To describe a circle with any center and distance.
- That all right angles are equal to one another.
- That if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less that two right angles.*
Two Equivalent versions of Euclid’s fifth postulates
There are three hypotheses which are
- hypothesis of right angles
- hypothesis of obtuse angles
- hypothesis of acute angles
- The first hypothesis is called as play fair’s axiom which is equivalent version of Euclid’s fifth postulate.
The second hypothesis states that a piece of straight line can be extended. The hypothesis of acute angle is extremely false because the acute angles are repulsive to the straight line.
