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

Glide to success with Doorsteptutor material for ISAT : Get full length tests using official NTA interface: all topics with exact weightage, real exam experience, detailed analytics, comparison and rankings, & questions with full solutions. ∠ ABC = ∠ ACB, ∠ 3 = ∠ 4. Show That ∠ 1 = ∠ 2

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 AC = DC, CB = CE. Show That AB = DE

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 ABC = ? ACB, ? 3 = ? 4. Show That? 1 = ? 2

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 . AB = BC, M Mid-Point of AB& N Mid- Point of BC

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) ]