Axioms are assumed statements. From these,
the structure is slowly built using proofs, based on
theses axioms and the other proven theorems. Euclid
built his system on 5 axioms, which he called
postulates . The first one was:
EUCLID'S POSTULATE
1: For every point P and for every point Q
not equal to P, there exists a unique line 
that passes the P and Q. This postulate is sometimes
stated as "two points determine a unique line."
However, this postulate makes the assumption that
there exists a point on a given line
. And none of Euclid's postulates determine whether or
not there exits a point not lying on a given line
.
Three axioms, which are called
Incidence
Axioms are needed:
1) For every point P and for every point Q
not equal to P, there exists a unique line
that passes the P and Q.
2) For every line ,
there exist at least two distinct points that lie
on the line .
3) There exist three points with the property
that no one line is incident with all three of
them.
The first axiom is the same as Euclid's and forces
all lines in Euclidean geometry to be straight lines.
In other words, the following example of two lines
passing through the same two points is impossible.
The second axiom asserts that there are points on a
line, and the third example asserts that more than a
line or space exists.
EUCLID'S POSTULATE
II: For every segment AB and for every
segment CD, there exists a unique point E such that B
is between A and E and segment CD is congruent to
segment BE.
This was his only congruence theorem which left out
the congruence of triangles. So, another axiom,
a Congruence
Axiom, is needed:
If two sides and the included angle of one
triangle are congruent respectively to two sides
and the included angle of another triangle, then
the two triangles are congruent.
and 
meet at a point P, as shown below. Then <APC
<BPD and <APD 