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Euclid’s fourth axiom says that everything equals itself. Is the given statement true or false? Justify your answer

Solution:
We know that

Euclid’s fourth axiom is “Things which coincide with one another are equal to one another”

In other words “Everything equals itself”

Therefore, the statement is true.

✦ Try This: Raksha and Deeksha have the same weight. If they each gain weight by 15 kg, how will their new weights be compared ?

Given, Raksha and Deeksha have the same weight.

We have to compare their new weights when each of them gains 15kg.

Let the weight of Raksha be x kg

So, weight of Deeksha = x kg

When each gain weight by 15kg,

Weight of Raksha = (x + 15) kg

Weight of Deeksha = (x + 15) kg

Using Euclid’s second axiom,

If equals are added to the equals, the wholes are equal.

From the Euclid’s axiom,

(x + 15) = (x + 15)

Therefore, the weight of Raksha is equal to the weight of Deeksha.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5

NCERT Exemplar Class 9 Maths Exercise 5.2 Sample Problem 1(v)

Euclid’s fourth axiom says that everything equals itself. Is the given statement true or false? Justify your answer

Summary:

Euclid used the term postulate for the assumptions that were specific to geometry and otherwise called axioms. The statement “Euclid’s fourth axiom says that everything equals itself” is true

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