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.'' c. 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.