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Determine if l, vertical bar, vertical bar, ml∣∣m. If yes, state the converse that proves the lines parallel

Answer
Attempt 1 out of 100
Multiple Choice Answers
Not parallel
l, vertical bar, vertical bar, ml∣∣m by Converse of alternate interior angles
l, vertical bar, vertical bar, ml∣∣m by Converse of alternate exterior angles
l, vertical bar, vertical bar, ml∣∣m by Converse of same side interior angles
l, vertical bar, vertical bar, ml∣∣m by Converse of same side exterior angles
l, vertical bar, vertical bar, ml∣∣m by Converse of corresponding angles

1 answer

To determine if lines \( l \) and \( m \) are parallel, we need to identify whether any of the angle relationships formed by a transversal intersecting those lines indicate that the lines are parallel.

Let’s analyze the situations considering the possible conclusions based on various angle relationships:

  1. Converse of Alternate Interior Angles: If two lines are cut by a transversal and the alternate interior angles are equal, then the lines are parallel.

  2. Converse of Alternate Exterior Angles: If two lines are cut by a transversal and the alternate exterior angles are equal, then the lines are parallel.

  3. Converse of Same Side Interior Angles: If two lines are cut by a transversal and the same side interior angles are supplementary (add up to 180 degrees), then the lines are parallel.

  4. Converse of Same Side Exterior Angles: If two lines are cut by a transversal and the same side exterior angles are supplementary, then the lines are parallel.

  5. Converse of Corresponding Angles: If two lines are cut by a transversal and the corresponding angles are equal, then the lines are parallel.

You will need to identify which of these angle relationships is present in your specific scenario to prove that lines \( l \) and \( m \) are parallel.

If you have the information about angles made by the transversal and how they relate to each other, select the correct answer:

  • If alternate interior angles are equal, you would conclude that \( l \parallel m \) by the Converse of Alternate Interior Angles.
  • If alternate exterior angles are equal, the conclusion would follow similarly but using the corresponding converse.
  • If the same side interior angles are supplementary, you'd use the Converse of Same Side Interior Angles.
  • If same side exterior angles are supplementary, then by that specific converse, the conclusion holds.
  • If corresponding angles are equal, you would conclude through that converse.

In your case, check the angle relationships at hand and pick the corresponding choice that indicates the correct conclusion based on one of the converses mentioned above.

If you don't have angle figures mentioned, it's not possible to conclude without additional information, and the answer would then be "Not parallel."