# NCERT Mathematics Class 9 Exemplar Ch 5 Introduction to Euclid՚S Geometry Part 7 (For CBSE, ICSE, IAS, NET, NRA 2022)

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9. In the Fig, we have , . Show that .

Answer: Given that: and According to Euclid՚s axioms, if equal are subtract from equals, then reminders are also equal. On subtracting equation (ii) from equation (i) , we get ➾

10. In the Fig. , we have , . Show that .

Answer: Given that: and According to Euclid՚s axioms, if equals are added to equals, the then wholes are also equal. So, on adding equation (i) and equation (ii) , we get ➾

11. In the Fig, if , and , show that .

Answer: Given that: ➾ and ➾ and According to Euclid՚s axioms, things which are double of the same things are equal to one another. On multiplying equation (iii) by 2, we get ➾ [From (i) and (ii) ]

12. In the Fig. :

(i) , M is the mid-point of AB and N is the mid- point of BC. Show that .

(ii) , M is the mid-point of AB and N is the mid-point of BC. Show that .

Answer: (i) Given that: is the mid – point of AB. ∴ and N is the mid – point of BC ∴ According to Euclid՚s axioms, things which are halves of the same things are equal to one another. From Equation (i) , we get On multiplying both sides by , we get ➾ [using (ii) and (iii) ] (ii) Given that: M is the mid – point of AB ∴ ➾ and N is the mid – point of BC ∴ ➾ According to Euclid՚s axioms, things which are doubles of the same things are equal to one another. On multiplying both sides of equation (i) by 2, we get ➾ [using (ii) and (iii) ]