Multiple Choice on Proof statement...help!!!?

Question

It is important to ask a key question when attempting to prove a statement. For the key question, "How can I show that 2 lines in a plane are parallel?" which of the following answers is incorrect? Explain why
a. Show that the slopes of the two lines are the same
b. Show that each of the lines is parallel to a third line
c. Show that the lines are on opposite sides of a quadrilateral
d. Show that each of the 2 lines is perpendicular to a third line

Answer 1

"How can I show that 2 lines in a plane are parallel?"
which of the following answers is incorrect? Explain why

Let's examine them one at a time:

a. Show that the slopes of the two lines are the same

Parallel lines have the same slope -- It's part of their definition. This one works. Next?

b. Show that each of the lines is parallel to a third line

Like the Transitive Property says, if A=B and B=C, then A=C. This goes for slopes of lines as well, so this one also works.

c. Show that the lines are on opposite sides of a quadrilateral

But who says that all quadrilaterals have parallel opposite sides? A trapezoid is a quadrilateral, but in almost all cases the left side and the right side are anything but parallel. I think this is the "wrong answer" that you're looking for. Let's examine "d" just to be sure...

d. Show that each of the 2 lines is perpendicular to a third line

Similar to answer "b" -- Perpendicular lines have slopes that are opposite reciprocals of each other (like 2 and -.5), so if both of the lines inquestion are perpendicular to line #3, then they must be parallel to each other.

Make sense? I hope this helps.

Barjesse37

Answer 2

c is incorrect because intersecting lines can have any polygon between them and intersecting lines are not parallel.

Answer 3

c. Consider any quadrilateral that isn't a parallelogram -- lines on opposite sides of it may very well intersect.