CLASS IX 
                           MATHEMATICS WORKSHEET 
                   CH 5 “INTRODUCTION TO EUCLID’S GEOMETRY” 
     VERY SHORT ANSWER TYPE QUESTIONS 
     Q.1 In how many chapters did Euclid divide his famous treatise “The elements”? 
     Q.2 It is known that if a = 2b and c = 2b, then a = c. Which Euclid’s axiom illustrates this statement? 
     Q.3 State Euclid’s fifth axiom. 
     Q.4 It is known that if x + y = 10, then x + y + z = 10 + z. Which axiom of Euclid does this statement 
        illustrate? 
     Q.5 State Euclid’s first postulate. 
     SHORT ANSWER TYPE QUESTIONS 
     Q.6 Solve the equation u – 5 = 15 and state the axiom that you use here. 
     Q.7 In figure, AC = XD, C is the mid-point of AB and D is the mid-point of XY. Using a Euclid’s axiom, 
        show that AB = XY. 
                                                 
     Q.8 In the figure, if ∠1 = ∠3, ∠2 = ∠4 and ∠3 = ∠4, write the relation between ∠1 and ∠2, using a 
        Euclid’s axiom. 
                                                 
     LONG ANSWER TYPE QUESTIONS 
                                                           1
     Q.9 If a point O lies between two points P and R such that PO = OR then prove that PO =   PR. 
                                                           2
     Q.10 Prove that every line segment has one and only one mid-point. 
     Q.11 Does Euclid’s fifth postulate imply the existence of parallel lines? Explain. 
                                       
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                                                               ANSWERS 
         1.     13 chapters                         
         2.     Sixth axiom                                                   
         3.     The whole is greater than the part.                          
         4.      Second axiom 
         5.      A straight line may be drawn from any point to any other point. 
         6.      u = 20 
         8.      ∠1 = ∠2 
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