Question

If x=2z and y=2z ,then x=y . Which Euclid's axiom is illustrated here ?

Answer 1

Here,Euclid's first axiom is illustrated.The first axiom is :- " Things which are equal to same thing are also equal to one another.

Answer 2

Given :  It is known that if x = 2z and y = 2z, then x = y

(1) Things which are equal to the same thing are equal to one another.

(2) If equals are added to equals, the wholes are equal.

(3) If equals are subtracted from equals, the remainders are equal.

(4) Things which coincide with one another are equal to one another.

(5) The whole is greater than the part.

(6) Things which are double of the same things are equal to one another.

(7) Things which are halves of the same things are equal to one another

To Find : Euclid's axiom that  illustrates the statement

(a) Second axiom

(b) fourth axiom

(c) sixth axiom

(d) seventh axiom

Solution:

x = 2z  ( x is double of z)

y = 2z,  (y is double of z)

then x = y  ( they are equal to each other )

(6) Things which are double of the same things are equal to one another.

in given options sixth axiom   illustrates the statement  

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