NCERT Mathematics Class 9 Exemplar Ch 5 Introduction to Euclid's Geometry Part 6

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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

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

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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

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

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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

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

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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