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RE: Can two parallel lines meet?
I'm a bit confused on the letters you used in the proof. Did you replace the angles α, β, γ, and δ with some other letters?
I'm a bit confused on the letters you used in the proof. Did you replace the angles α, β, γ, and δ with some other letters?
Thanks @greenrun for the feedback, the proof only considered simple linear equation:
Ax+Bx+C = 0, and
Ax+Bx+D = 0.
(general equation for a straight line . i.e line CD AND line AB)
when we solve this, it gives w(C-D) =0, WHERE w =0, and C-D = 0, AND C=D. This means line C = D, AND w= 0. then if C= D, THEN two lines are identical (overlapped).
Recall
This results in making a point in cartesian coordinates (x,y) to becomes (x, y, w)
substituting w = 0. in this equation gives (x,y) in cartesian to becomes (x, y, w) = (x/w, y/w) = (∞,∞). and this condition justifies that line C can only meet line D at (∞,∞) since w(C-D) = 0.
The proof does not consider/replace the angles α, β, γ, and δ but based on simple linear equation of a straight line.
Now that's clearer. Thank you.
It's my pleasure!