A transversal intersects a pair of parallel lines. Decide whether each statement is...
Check the final answer first, then review the worked steps.
Problem
A transversal intersects a pair of parallel lines. Decide whether each statement is true or false.
Answer
True, False, True
Step-by-step solution
- Analyze the first statement: The statement is "Alternate exterior angles are always congruent." When a transversal intersects two parallel lines, alternate exterior angles are on opposite sides of the transversal and outside the parallel lines. These angles are indeed always congruent. Therefore, this statement is true.
- Analyze the second statement: The statement is "Corresponding angles are always supplementary." Corresponding angles are in the same position at each intersection where a transversal crosses two lines. When the lines are parallel, corresponding angles are congruent, not supplementary. Supplementary angles add up to 180 degrees. Therefore, this statement is false.
- Analyze the third statement: The statement is "Same-side interior angles are always supplementary." Same-side interior angles are on the same side of the transversal and between the parallel lines. When a transversal intersects two parallel lines, same-side interior angles are always supplementary (they add up to 180 degrees). Therefore, this statement is true.