Question

can someone check my proof for correct logic

Answer 1

prove: if the sum of the angles of a triangle is a constant n, then n=180 and thus the geometry is Euclidean.
proof: consider triangle ABC with measure of angle 2+4+5=n where n is a constant. Then construct a line l through B such that l is parallel AC. Then if the measure of angle 1+2+3=180 and by the converse of the AIAT (alternate interior angle theorem) angle 1=4 and angle 5=3. So measure of angle 4+5+2=180 and thus n=180 and this is an Euclidean geometry.

Answer 2

if the triangles angle sum = 180 it is euclidean, but it does not have to equal 180.
In my proof i wrote "Then if the measure of angles 1+2+3=180" does this count as a proof.

Answer 3

if the triangles angle sum = 180 it is euclidean, but it does not have to equal 180. In my proof i wrote "Then if the measure of angles 1+2+3=180" does this count as a proof.