Question

8. In ∆ABC, X and Y are the points on AB and BC such that BX = BY
and AB=BC. Prove that AX=CY. State the Eculid's Axiom used?​

Answer 1

ANSWER:-

Given:

In ∆ABC, X & Y are the points on AB & BC such that BX = BY & AB = BC.

To prove:

AX = CY.

Proof:

Above attachment a diagram.

Given;

AB= BC.............(1)

BX = BY.............(2)

So,

Subtract the two equation (1) & (2),we get;

=) AB - BX = BC -BY

=) AX = CY [proved]

[since, from the diagram we can observe that when BX is subtracted from AB,we are left with AX, similarly, when BY is subtracted from BC, we are left with CY.]

Thus,

This is the result of Euclid's second axiom that states, if the equals are subtracted from equals, then the remainder is also equal.

Hope it helps ☺️

Answer 2

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Given:

AB = BC...... 1

and BX = BY..........2

To prove:

We need to prove that AX = CY

Proof:

Subtracting (2) from (1)

AB - BX = BC - BY

$\implies$ AB - BX = CB - BY

$\implies$ AX = CY

$\therefore$ BC = CB

Euclid's Axiom :- If equals are subtracted from equals, the remainders are equal.