Question

Which statement best compares the method of constructing a pair of parallel lines with the method of constructing a pair of perpendicular lines?

Both require the construction of congruent angles.

Both require the construction of angle bisectors.

Both use the straightedge to measure the length of the arcs.

Both use the compass to draw arcs from points.

Answer 1

both require the construction of angle bisectors.

Answer 2

I'd go with Both use the compass to draw arcs from points.

Answer 3

Who is correct?

Answer 4

why? if you used a compass you would just essentially be doing it to find a perpendicular bisector to the line...

Answer 5

but for parallels you don't ;)

Answer 6

how would you draw it? I would take the perpendicular bisector to the line, then take the perpendicular bisector to the line again in a different spot to draw the parallel

Answer 7

for the paralel with a compass you could just draw two circles and connect the tangent lines

Answer 8

Alright then :)

Answer 9

I guess the question then is is it possible to construct a parallel line without taking the bisector? I think if you used the compass that would still technically be creating a bisector since you are just measuring the distance r from the line and this is obvioulsy going to be at angle \(\frac{\pi}{2}\) so you are indirectly creating a bisector.

Answer 10

same as if you used the intersection of two lines that are not bisectors. you would again just indirectly be taking the bisector of the line. I cannot think of any other way to do this.