non-Euclidean geometries chapter 5 can study by students of class 9. These definitiona and formulas of Class 9 Maths Chapter 5: Introduction to Euclid’s Geometry is developed and witten by our expert teachers. Maths formulas. non-Euclidean geometries is prepapred and collected from varius resources to help the students.
All the attempts to prove Euclid’s fifth postulate using the first 4 postulates failed. But they led to the discovery of several other geometries, called non-Euclidean geometries.
Theorem 5.1 : Two distinct lines cannot have more than one point in common.
Proof : Here we are given two lines l and m. We need to prove that they have only one point in common.
For the time being, let us suppose that the two lines intersect in two distinct points, say P and Q. So, you have two lines passing through two distinct points P and Q. But this assumption clashes with the axiom that only one line can pass through two distinct points. So, the assumption that we started with, that two lines can pass through two distinct points is wrong.
We are forced to conclude that two distinct lines cannot have more than one point in common
