Understanding Parallel Lines and Transversals
(True or False)
1. If two lines are intersected by a transversal and alternate interior angles are equal in measure, then the lines are parallel.
2. If two lines are intersected by a transversal and consecutive interior angles are equal in measure, then the lines are parallel.
3. If two lines are intersected by a transversal and vertical angles are equal in measure, then the lines are parallel.
Final answer:
It is true that if alternate interior angles formed by a transversal are equal, the lines are parallel. However, the statements regarding consecutive interior angles and vertical angles as conditions for parallelism are false.
Explanation:
True or False: 1. If two lines are intersected by a transversal and alternate interior angles are equal in measure, then the lines are parallel. True. When alternate interior angles are equal, this is one of the conditions confirming the lines are parallel, according to the parallel postulate in geometry.
2. If two lines are intersected by a transversal and consecutive interior angles are equal in measure, then the lines are parallel. False. Consecutive interior angles being equal actually suggests the lines are the same line (coincident), not parallel.
3. If two lines are intersected by a transversal and vertical angles are equal in measure, then the lines are parallel. False. Vertical angles are always equal in measure, regardless of whether the lines are parallel or not, so this condition does not guarantee the lines are parallel.
If you have two parallel lines intersected by a transversal, what can you say about the corresponding angles? When two parallel lines are intersected by a transversal, the corresponding angles are congruent or equal in measure.