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

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)]

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