ieatStairs
New member
- Joined
- Jul 1, 2017
- Messages
- 2
Hello!
I'm taking a geometry course, and was assigned a project where we have to make some constructions, using ONLY two parallel edges of a straightedge. (No compass or measurements.) There constructions are:
Construction 1: Construct the angle bisector of a given angle. Show your method works on both acute and obtuse angles.
Construction 2: Construct a perpendicular bisector of a given segment (where the length of the given segment is greater than the distance between your parallel lines.)
Construction 3: Construct the perpendicular through a given point on a given line.
Construction 4: Construct a perpendicular bisector of a given segment (where the length of the given segment is less than the distance between your parallel lines.
Construction 5: Construct a line parallel to a given line through a given point not on the given line.
Construction 6: Construct a perpendicular to a given line through a given point not on the given line.
I've tried creating 1 & 2, and I think I've gotten somewhere by creating a rhombus and following its properties, but I'm not really sure how to prove all the side lengths are equal.
On the other ones, I tried creating a few, but I always end up with something like, "how can I be sure that this angle is 90 degrees," or "how can I be sure that this line is half the length of another?"
I'm struggling on these, and if anyone can give me some hints or point me in the right direction on any of the constructions, that would be greatly appreciated.
Thanks!
P.S. Here is a link to the assignment, the uploader wouldn't work for me so here:
< link to objectionable site removed >
I'm taking a geometry course, and was assigned a project where we have to make some constructions, using ONLY two parallel edges of a straightedge. (No compass or measurements.) There constructions are:
Construction 1: Construct the angle bisector of a given angle. Show your method works on both acute and obtuse angles.
Construction 2: Construct a perpendicular bisector of a given segment (where the length of the given segment is greater than the distance between your parallel lines.)
Construction 3: Construct the perpendicular through a given point on a given line.
Construction 4: Construct a perpendicular bisector of a given segment (where the length of the given segment is less than the distance between your parallel lines.
Construction 5: Construct a line parallel to a given line through a given point not on the given line.
Construction 6: Construct a perpendicular to a given line through a given point not on the given line.
I've tried creating 1 & 2, and I think I've gotten somewhere by creating a rhombus and following its properties, but I'm not really sure how to prove all the side lengths are equal.
On the other ones, I tried creating a few, but I always end up with something like, "how can I be sure that this angle is 90 degrees," or "how can I be sure that this line is half the length of another?"
I'm struggling on these, and if anyone can give me some hints or point me in the right direction on any of the constructions, that would be greatly appreciated.
Thanks!
P.S. Here is a link to the assignment, the uploader wouldn't work for me so here:
< link to objectionable site removed >
Last edited by a moderator: