Two parallel lines bisected by a straight line can produce three angles. Angles on the one side or 'inside' are corresponding. They can also be co-interior, in that they add up to 180-degrees. Opposite side one are called alternate angles.
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When Two parallel lines are cut by the transversal, __________ angles are supplementary
If two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is the transversal postulate. So the answer is the lines would be parallel. This means that the statement is true.
When 2 parallel lines are cut by a transversal some of the pairs of angles which are formed are called alternate angles whereas other pairs are called interior angles.
A transversal is simply any line that passes through two or more coplanar lines each at different points. So picture, if you will, two lines that are clearly not parallel. I can easily construct a transversal that passes through them. HOWEVER, if two parallel lines are intersected by a transversal, then the corresponding angles are congruent. This is called the transversal postulate. If the corresponding angles are congruent, than the lines are parallel. This is the converse of the first postulate. So, the answer to your question is NO, unless the corresponding angles are congruent.
Only if the lines cut by the transversal are parallel.