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In the figure,we have: $AC = XD$,$C$ is the mid-point of $AB$ and $D$ is the mid-point of $XY$. Using Euclid's axiom,show that $AB = XY$.

$A$ surface is that which has $\ldots \ldots \ldots$ only.

State whether the following statement is True or False and justify your answer:
Euclid's fourth axiom states that things which coincide with one another are equal to one another.

Solve the following question using an appropriate Euclid's axiom:
In the figure,we have $\angle ABC = \angle ACB$ and $\angle 3 = \angle 4$. Show that $\angle 1 = \angle 2$.

State whether the following statement is True or False. Justify your answer.
Attempts to prove Euclid's fifth postulate using the other postulates and axioms led to the discovery of several other geometries.

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