Proof that an angle across line is equal to 180 degrees

Question

When given a straight line, how do you prove that an angle across it is equal to 180 degrees, or two right angles?

It feels like something that should be an axiom, but it isn't one of the 5 postulates of Euclidean geometry. I suspect the proof is related to the axiom about all right angles being similar, but I don't know how to use that in proving the angle on a line. Can anyone help me?

I doubt I'm the first person to ask this, but I couldn't find any question similar to mine on this website.

I think it's proposition 13 in book 1 – danimal Jun 04 '15 at 14:50 — danimal, Jun 04 '15 at 14:50
what is your definition of degree measure? – abel Jun 04 '15 at 15:55 — abel, Jun 04 '15 at 15:55

score 1 · Answer 1 · answered Jun 04 '15 at 15:33

1

We know how to form an isoceles triangle CAB on a given side of a line segment AB. Also we know how to form another such triangle DAB on the other side. Joining CD we see that it intersect AB in a middle point E. Now using SAS we get two adjacent angles along a line which are congruent. Call the measure of each 90 and so we get 180 for...

answered Jun 04 '15 at 15:33

Adelafif

1,275

Not sure what you're saying at all here... Using triangles to prove that a line is 180 degrees would appear to be circular reasoning too. – Cataline Jun 04 '15 at 18:22

Proof that an angle across line is equal to 180 degrees

1 Answers1