# NCERT Mathematics Class 9 Exemplar Ch 5 Introduction to Euclid's Geometry Part 7

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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)]