How do I prove that tangents to a circle at the endpoints of a diameter are parallel.?

Question

I have to state what is given, what is to be proved and plan the proof.

it has to be a two cloumn proof.

Answer 1

given a circle centre O and diameter AB
given tangents to the circle at A and B
TPT the two tangents are parallel
Proof.tangent at A will be perpendicular to AB(property of tangents)
tangent at B perpendicular to AB (property of tangents)
thus the two tangents are both perpendicular to AB
lines perpendicular tithe same line must be parallel
therefore the tangents are parallel

Answer 2

Since the lines are tangents to a circle, they are perpendicular to the radius of the circle at each point of tangency. The endpoints of a diameter are simply the endpoints of two radii. Therefore the two tangent lines form a 90 degree angle with the diameter at each endpoint of the diameter. Furthermore, the diameter is a transversal between the two tangent lines. It's sufficient to prove that the transversal line and the tangent lines create alternate interior angles between them which are not only equal, but 90 degrees in measure.

I believe you can take it from here.

Answer 3

well you know that a tangent to the diameter is a right angle. so on both sides they are right angles. Opposite interior angles congruent implies parallel lines.
Just put those steps into a two column proof and you are done

Answer 4

Tangent to a circle are perpindicular to the radius at the point of tangence. Tangents to a diameter are both perpindicular to that diameter. lines perpindicular to the same line are parallel, therefore the tangents are parallel.

Answer 5

If two lines are perpendicular to one line then they are parallel to each other.

In this case, both tangents are perpendicular to the diameter, therefore, they are parallel to each other.

Answer 6

I like the explanation Raj gave. I would say the same thing!