Question

Which statement best shows the similarity in constructing a pair of parallel lines and a pair of perpendicular lines?

Both require the use of a straightedge to join points.

Both require the construction of congruent angles at a given point.

Both do not require the use of a compass to draw arcs.

Both do not require the construction of a bisector of an angle or line segment.

Answer 1

parallel line:
http://www.mathopenref.com/constparallel.html

perpendicular line:
http://www.mathopenref.com/constperplinepoint.html

Answer 2

Let's take a look at each one:

*Both require the use of a straight edge to join point. Is this true? Well parallel lines never touch each other at a point so this statement saying that "both" parallel and perpendicular lines join at a point is false.

*Both require the construction of congruent angles at a given point. Is this true? Again, parallel lines do not meet at a point anywhere since parallel lines never touch each other, so this is also false.

*Both do not require the use of a compass to draw arcs. Is this true? Perpendicular lines are straight lines with no arcs, and parallel lines are also straight lines that don't have arcs. This is a true statement.

*Both do not require the construction of a bisector of an angle or line segment. Is this true? Bisecting implies that you are crossing the lines somewhere and, again, parallel lines never cross or touch each other in any way; they just run side by side forever, so this is a false statement.

So the third one is true.