Ch 5 introduces Euclid's axiomatic approach to geometry. Students learn about definitions, axioms (common notions), postulates, and theorems — the logical framework that underpins all of geometry.
Axioms are universal truths accepted without proof (e.g., "things equal to the same thing are equal"). Postulates are assumptions specific to geometry (e.g., "a straight line can be drawn from any point to any other point"). Theorems are statements proved using axioms and postulates.
1. A straight line may be drawn from any one point to any other. 2. A terminated line (segment) can be extended indefinitely. 3. A circle can be drawn with any centre and radius. 4. All right angles are equal to one another. 5. If a straight line falling on two lines makes interior angles on the same side less than two right angles, the two lines, if extended, meet on that side.
Download: https://ncert.nic.in/textbook/pdf/iemh105.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
It states: if a line crosses two other lines making the sum of interior angles on one side less than 180°, those two lines will eventually meet on that side. This is equivalent to saying: through a point not on a line, exactly one parallel line exists.
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