Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries. Is the given statement true or false? Justify your answer
Solution:
“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 taken together less than two right angles.”
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.
These are quite different from Euclidean geometry and are known as non-Euclidean geometry.
Therefore, the statement is true.
✦ Try This: It is known that x + y = 11 and that x = z. Show that z + y = 11. Solve using Euclid’s axiom
Given, x + y = 11 --------- (1)
Also, x = z ------------------ (2)
We have to show that z + y = 11
Using Euclid’s second axiom,
If equals are added to the equals, the wholes are equal.
From (2),
x + y = z + y
From (1).
z + y = 15
Therefore, z + y = 11
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5
NCERT Exemplar Class 9 Maths Exercise 5.2 Problem 9
Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries. Is the given statement true or false? Justify your answer
Summary:
The statement “Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries” is true
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