Help with Geometry Proof!

[katiedecan]

Hello! This is actually the first time I've used this forum - I hope one of you can help me!

Here's the problem:

Claire claims that she discovered the following procedure for constructing a line through a given point P parallel to a given line l. She would like to know how to prove that her construction is correct. How do you respond?

Claire: I choose any point Q on line l and construct the perpendicular bisector of line PQ, intersecting l at S and line PQ, at M. I find point T on line SM such that MT = MS. The line PT is parallel to l.

I have attached a photo of the problem itself, including the construction. Please let me know if you have any problems/questions!

Thank you!

Katie

 

[Steven G]

Hello! This is actually the first time I've used this forum - I hope one of you can help me!

Here's the problem:

Claire claims that she discovered the following procedure for constructing a line through a given point P parallel to a given line l. She would like to know how to prove that her construction is correct. How do you respond?

Claire: I choose any point Q on line l and construct the perpendicular bisector of line PQ, intersecting l at S and line PQ, at M. I find point T on line SM such that MT = MS. The line PT is parallel to l.

I have attached a photo of the problem itself, including the construction. Please let me know if you have any problems/questions!

Thank you!

KatieView attachment 5308

Katie, this is a math help forum and we have volunteers who are willing to help you with your proof. However we will not just do the proof for you. What have you tried? Where are you stuck? How does one usually prove that two lines are parallel?