What is the same-side interior angles postulate?

Answer 1

Technically this does not exist. Many math texts use it as a shortcut to introduce properties of angles for parallel lines that are cut by a transversal.

It says that when lines are parallel and are cut by a transversal, then the same side interior angles must be supplementary (add up 180 degrees).

Once you say this is a postulate (assumed to be true), then you can prove other things like the Congruent Corresponding Angles theorem that says "If lines are parallel and are cut by a transversal, then the corresponding angles must be conguent."

Some texts do the reverse and say Corresponding Angles is a postulate and then prove Same-Side Interior as a Theorem.

Euclid proved both these using his 5th Postulate (often re-written as the Parallel Postulate or Playfair's Axiom). To do this, he had to prove that the interior angles of a triangle sum to 180. Since many Math Texts do not introduce this fact until later chapters, they take this shortcut of "assume the Same-Side Interior" is true and the remaining theorems are much easier. Another reason Math books may take this shortcut is that Euclid's method is usually done by proof by contradiction - which is sometimes more difficult to understand.

I believe the Khan Academy video of this material is done correctly.