Solve the following question using appropriate Euclid's axiom:
It is known that $x+y=10$ and that $x=z$. Show that $z+y=10$.

Solve the following question using appropriate Euclid's axiom:
In the figure:
$BM = BN$,$M$ is the mid-point of $AB$ and $N$ is the mid-point of $BC$. Show that $AB = BC$.

Give a definition for the radius of a circle. Are there other terms that need to be defined first? What are they,and how might you define them?

State whether the following statement is true or false:
There are an infinite number of lines which pass through two distinct points.

Consider two 'postulates' given below:
$(i)$ Given any two distinct points $A$ and $B$,there exists a third point $C$ which is in between $A$ and $B$.
$(ii)$ There exist at least three points that are not on the same line.
Do these postulates contain any undefined terms? Are these postulates consistent? Do they follow from Euclid's postulates? Explain.

Euclid stated that all right angles are equal to each other in the form of