NCERT Mathematics Class 9 Exemplar Ch 5 Introduction to Euclid՚s Geometry Part 6 (For CBSE, ICSE, IAS, NET, NRA 2022)

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6. In the Fig. 5.6, we have

and

. Show that .

Figure Shows BX = 1/2 AB, by = 1/2 BC, and AB = BC

Answer: Given that: ➾ and ➾ and On putting the values from equations (i) and (ii) in equation (iii) , we get According to Euclid՚s axioms, things which are double of the same things are equal to one another. ∴

7. In the Fig. 5.7, we have , . Show that .

∠ 1 = ∠ 2, ∠ 2 = ∠ 3. Show That ∠ 1 = ∠ 3

Answer: Given that: and According to Euclid՚s axioms, things which are equal to the same thing are equal to one another. From equations (i) and (ii) , we get

∠ 1 = ∠ 3 and ∠ 2 = ∠ 4. Show That ∠ a = ∠ C

8. In the Fig. 5.8, we have and . Show that .

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