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.

Respuesta :

Literally, parallel lines are lines that extends in both directions without meeting.

The three definitions of parallel lines are correct, but Rachel's and Briana's definitions have flaws

Rachel

The definition implies that two lines are said to be parallel if they are both perpendicular to another line.

This definition is correct, but the definition brings a new concept; it introduces the concept of line transversal.

Because the parallel lines can be defined without introducing the concept of line transversal (which was not part of the required definition), then we can conclude that the definition has a drawback.

Alex

Alex's definition is correct, and it has no drawback because the definition can  be applied to concepts where parallel lines are used.

Briana

Here, Brianna introduced the concept of slopes.

Ideally, parallel lines have the same slope; but the concept is limited to slopes only; and cannot be applied to other concepts such as transversal of lines.

See illustration of parallel lines

Read more about parallel lines at:

https://brainly.com/question/2456036

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