Alex and his friends are studying for a geometry test and one of the main topics covered is parallel lines in a plane. They each write down what they think it means for two distinct lines in a plane to be parallel : a. Rachel writes, "two distinct lines are parallel when they are both perpendicular to a third line." b. Alex writes , " two distinct lines are parallel when they do not meet ." Briana writes , "two distinct lines are parallel when they have the same slope." Analyze each definition , indicating if it is mathematically correct and if it has any drawbacks.