Hello, proofsRkickingmybutt!
Prove that the tangents to a circle at the endpoints of a diameter are parallel.
State what is given, what is to be proved, and your plan of proof.
Then write a twocolumn proof. Code:
A
P     * * *     Q
*  *
*  *
*  *

*  *
* *O *
*  *

*  *
*  *
*  *
R     * * *     S
B
There is a Theorem that says:
. . If a line is tangent to a circle, the radius drawn to
. . the point of tangency is perpendicular to the tangent.
We have a circle with center $\displaystyle O$ and diameter $\displaystyle AB.$
Line $\displaystyle PQ$ is tangent to circle $\displaystyle O$ at $\displaystyle A.$
Line $\displaystyle RS$ is tangent to circle $\displaystyle O$ at $\displaystyle B.$
$\displaystyle 1.\;OA \perp PQ,\:OB \perp RS$ . . . . . $\displaystyle \text{Theorem}$
$\displaystyle 2.\;\angle OAP = 90^o,\:\angle OBS = 90^o$ . .$\displaystyle \text{d{e}f. perpendicular}$
$\displaystyle 3.\;\angle OAP = \angle OBS$. . . . . . . . .$\displaystyle \text{All right angles are equal.}$
$\displaystyle 4.\;\therefore\:PQ \parallel RS$. . . . . . . . . . . $\displaystyle \text{altint. angles}$