Prove that tangents to a circle at the endpoints of a diameter are parallel. Thank you!  

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Lines that are tangent to a circle are perpendicular to the radius at the point of tangency.  A diameter is formed by two radii that go in opposite directions from the center of the circle.  It is a straight line because the angle would be 180 degrees.  Since the tangent lines are perpendicular, the angles between the radii and tangent lines are 90 degree.  Since the diameter is a straight line, it is now a transversal line cutting across the two tangents.  The alternate interior angles are equal, they are both 90 degrees.  When a transversal cuts two lines and forms equal alternate interior angles, the two lines are parallel.