UPSC > NCERT Textbooks (Class 6 to Class 12) > Exercise 5.2 NCERT Solutions - Introduction to Euclid’s Geometry
Exercise 5.2 NCERT Solutions - Introduction to Euclid’s Geometry - NCERT Textbooks (Class 6 to Class 12) - UPSC
Question 1. How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
Solution: We can have: “Two distinct intersecting lines cannot be parallel to the same line.”
Question 2. Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
Solution: Yes, If a straight line ‘l’ falls on two lines ‘m’ and ‘n’ such that sum of the interior angles on one side of l is two right angles, then by Euclid’s fifth postulate, the lines will not meet on this side of l. Also we know that the sum of the interior angles on the other side of the line l will be two right angles too. Thus, they will not meet on the other side also.
∴ The lines ‘m’ and ‘n’ never meet, i.e., they are parallel.
The document Exercise 5.2 NCERT Solutions - Introduction to Euclid’s Geometry | NCERT Textbooks (Class 6 to Class 12) - UPSC is a part of the UPSC Course NCERT Textbooks (Class 6 to Class 12).
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FAQs on Exercise 5.2 NCERT Solutions - Introduction to Euclid’s Geometry - NCERT Textbooks (Class 6 to Class 12) - UPSC
| 1. What is Euclid's Geometry? |  |
Ans. Euclid's Geometry is a mathematical system developed by the ancient Greek mathematician Euclid. It is based on a set of axioms and postulates, which serve as the foundation for reasoning about geometric shapes and their properties.
| 2. What are the main components of Euclid's Geometry? | |
Ans. The main components of Euclid's Geometry are axioms, postulates, definitions, and propositions. Axioms are self-evident truths, postulates are statements accepted without proof, definitions establish the meaning of geometric terms, and propositions are proven statements based on logical reasoning.
| 3. How is Euclid's Geometry different from other geometries? | |
Ans. Euclid's Geometry, also known as Euclidean Geometry, is a branch of geometry that focuses on flat or two-dimensional shapes and their properties. It is based on a set of axioms and postulates, which are specific to Euclid's system. Other geometries, such as non-Euclidean geometries, have different sets of axioms and postulates, leading to different geometric interpretations.
| 4. What are some applications of Euclid's Geometry in real life? | |
Ans. Euclid's Geometry has various real-life applications. It is used in architecture, engineering, and design to create and analyze structures. It helps in surveying land and mapping physical spaces. It also plays a crucial role in computer graphics, where Euclidean principles are used to represent and manipulate objects in virtual environments.
| 5. Can Euclid's Geometry be applied to three-dimensional shapes? | |
Ans. Euclid's Geometry primarily deals with two-dimensional shapes. However, it forms the foundation for three-dimensional geometry as well. By extending the principles and concepts of Euclidean Geometry, it becomes possible to analyze and reason about three-dimensional shapes and their properties.
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