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Maths class 9 Introduction to Euclid’s Geometry
Tuesday, 4 June 2013
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Maths class 9 Introduction to Euclid’s Geometry
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Definitions, formula and notes of Euclid’s Geometry
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Introduction , Indian contribution in geometry ,Euclid’s Definitions, Euclid’s axioms, Euclid’s five postulates
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Theorem 5.1 : Two distinct lines cannot have more than one point in common.
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Equivalent Versions of Euclid’s Fifth Postulate
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Ncert Solution Exercise 5.1
1
Which of the following statements are true and which are false? Give reasons for youranswers.(i) Only one line can pass through a single point.(ii) There are an infinite number of lines which pass through two distinct points.(iii) A terminated line can be produced indefinitely on both the sides.(iv) If two circles are equal, then their radii are equal.(v) In Fig. 5.9, if AB = PQ and PQ = XY, then AB = XY.
2
Give a definition for each of the following terms. Are there other terms that need to bedefined first? What are they, and how might you define them?(i) parallel lines (ii) perpendicular lines (iii) line segment(iv) radius of a circle (v) square
3
Consider two ‘postulates’ given below:(i) Given any two distinct points A and B, there exists a third point C which is inbetween A and B.(ii) There exist at least three points that are not on the same line.Do these postulates contain any undefined terms? Are these postulates consistent?Do they follow from Euclid’s postulates? Explain.
4
If a point C lies between two points A and B such that AC = BC, then prove thatAC = 1/ 2 AB. Explain by drawing the figure.
5
In Question 4, point C is called a mid-point of line segment AB. Prove that every linesegment has one and only one mid-point.
6
In Fig. 5.10, if AC = BD, then prove that AB = CD.
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Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note thatthe question is not about the fifth postulate.)
Ncert Solution Exercise 5.2
1
How would you rewrite Euclid’s fifth postulate so that it would be easier to understand?
2
Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.
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