Without using angle measure how do I prove two lines are parallel to the same line are parallel to each other? I am currently using the book "Euclidean Geometry" by David M. Clark.
I have to prove that: two lines parallel to the same line are parallel to each other.
I am not allowed to use angle measure yet (degrees).
I am able to use any triangle congruence (SSS, SAS, AAS, ASA, HL)
I am allowed to use angle bisectors, midpoints, circles, right angles, isosceles triangles, vertical angles, corresponding angles, alternate interior angles, exterior angles, and squares to prove this.
We have these theorems which may be useful in proving this:


*

*If two lines have a transversal which forms alternative interior
angles that are congruent, then the two lines are parallel.

*If two lines have a transversal which forms corresponding angles that
are congruent, then the two lines are parallel.

*An exterior angle of a transversal is not congruent to either
opposite interior angle.

*Vertical angles are congruent.

*Congruent angles have congruent supplements.

*All right angles are congruent.

*Axiom 5: For every line l and every point P not on l, there is 
at most one line containing P that is parallel to l.
I started off drawing two parallel lines, l and m and point P on m, but I really don't even know where to begin.
Any help would be appreciated.

Draw a line parallel to A as B . Alternate angles a = b 
Draw a line parallel to A as C . Alternate angles a = c 
a = b = c
$ \because$ a = c, A is parallel to C by the converse thm, the first one in the given list.
