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If two lines are cut by a transversal and the alternate exterior angles are equa

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Question: If two lines are cut by a transversal and the alternate exterior angles are equal, what can be concluded about the lines?

Options:

  1. They are perpendicular.
  2. They are parallel.
  3. They intersect.
  4. They are skew.

Correct Answer: They are parallel.

Solution: 

If alternate exterior angles are equal, the lines are parallel.

If two lines are cut by a transversal and the alternate exterior angles are equa

Practice Questions

Q1
If two lines are cut by a transversal and the alternate exterior angles are equal, what can be concluded about the lines?
  1. They are perpendicular.
  2. They are parallel.
  3. They intersect.
  4. They are skew.

Questions & Step-by-Step Solutions

If two lines are cut by a transversal and the alternate exterior angles are equal, what can be concluded about the lines?
  • Step 1: Identify the two lines that are being cut by the transversal.
  • Step 2: Locate the alternate exterior angles formed by the transversal and the two lines.
  • Step 3: Check if the alternate exterior angles are equal in measure.
  • Step 4: If the alternate exterior angles are equal, conclude that the two lines are parallel.
  • Alternate Exterior Angles – Angles that are on opposite sides of a transversal and outside the two lines.
  • Parallel Lines – Lines that never intersect and are equidistant from each other.
  • Transversal – A line that intersects two or more lines at different points.
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