Prove that vertically opposite angles are equal .

Theorem: All vertically opposite angles have equal measure.

(To get started, we first use the definition of vertically opposite angles to make sense of the statement. We sketch a labeled figure to introduce notation. We then restate what must be shown using the explicit notation.)

Proof:

Let one pair of vertically opposite angles in the following figure have measures s and t and the other have measures u and v.

We must show s=t and u=v.

s+u=straight angle=t+u. Therefore s=t.

Likewise, s+u=straight angle=s+v. Therefore u=v.

 Thanks

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 Proove alternate interior angles equal

 Sorry param! by mistake I disliked! The solution for that yours is from the golden guide right? :P Anyways thank you!!

there is no proof of alternate angle as there is a alternate angle axiom which states that if two parallel lines are intersected by a transversal then the alternate angles are always equal