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

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**Exercise 5.3**

1. Two salesmen make equal sales during the month of August. In September, each salesman doubles his sale of the month of August. Compare their sales in September.

Answer: Let the equal sale of two salesmen in August be x. In September each salesman doubles his sale of August. Thus, sale of first salesman is 2x and sale of second salesman is 2x. According to Euclid’s axioms, things which are double of the same things are equal to one another. So, in September their sales are again equal.

2. It is known that and that x = z. Show that ?

Answer: We have, and According to Euclid’s axioms, if equals are added to equals, the wholes are equal. So, from statement (ii), we get x + y = z + y from equation (i) and (iii), we get

3. Look at the Fig. 5.3. Show that length sum of lengths of.

Answer: From the given figure, we have [AB, BC and CD are the parts of AD] Here AD is also the parts of AH. According to Euclid’s axioms, the wholes are greater than the part. i.e., So, Length sum of the length of.

4. In the Fig.5.4, we have, . Show that.

Answer: We have, and According to Euclid’s axioms, if equals are subtracted from equals, the remainders are Equal. So, on subtracting equation (ii) from equation (i), we get

5. In the Fig., we have X and Y are the mid-points of AC and BC and. Show that.

Answer: Given that X is the mid – point of AC ∴ ⟹ and Y is the mid – point of BC ∴ ⟹ Also given that According to Euclid’s axiom, things which are double of the same things are equal to one Another. From equation (iii), we get ⟹