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Answer :
The theorems which we need to prove to prove parallelism are:
1. Corresponding angles
2. Alternate angles
3. Opposite angles
4. Perpendicularity
How to prove parallelism ?
To prove parallelism
we need to prove any of the given points
1. Show that the angles that correspond are equal.
2. Convey the equality of different interior angles.
3. Make it clear that adjacent internal angles are complementary.
4. Show that the outer angles that follow each other are supplementary.
5. Demonstrate that the lines in a plane are perpendicular to the same line.
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Final answer:
To prove parallelism when lines are cut by a transversal, demonstrate that either alternate interior angles are equal or same-side interior angles are supplementary.
Explanation:
When proving that lines cut by a transversal are parallel, the angles you would need to show as supplementary (summing up to 180°) are either:
Alternate interior angles
Same-side interior (consecutive interior) angles.
If the alternate interior angles are equal, this implies parallelism by the Alternate Interior Angles Theorem. Conversely, if the same-side interior angles are supplementary, this implies parallelism by the Consecutive Interior Angles Theorem. Showing either of these conditions is sufficient to prove that two lines cut by a transversal are parallel to each other.
