NCERT Mathematics Class 9 Exemplar Ch 5 Introduction to Euclid's Geometry Part 4

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Exercise 5.2

1. Euclidean geometry is valid only for curved surfaces.

Answer: False, it is valid only for the figures in the plane.

2. The boundaries of the solids are curves.

Answer: False, boundaries of the solids are surfaces.

3. The edges of a surface are curves.

Answer: False, the edges of surfaces are line.

4. The things which are double of the same thing are equal to one another.

Answer: True, one of the Euclid’s axioms.

5. If a quantity B is a part of another quantity A, then A can be written as the sum of B and some third quantity C.

Answer: True, because of one of Euclid’s axioms.

6. The statements that are proved are called axioms.

Answer: False, statements that are proved are theorems.

7.”For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l “is known as Play fair’s axiom.

Answer: True, it is an equivalent version of Euclid’s fifth postulate.

8. Two distinct intersecting lines cannot be parallel to the same line.

Answer: True, it is an equivalent version of Euclid’s fifth postulate.

9. Attempts to prove Euclid’s fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

Answer: True, these geometries are different from Euclidean geometry.