Euclidean's basic constructions

[sheahowe]

I am having a hard time understanding how to do construction #7 of the basic constructions. It says to contruct a line parallel to a given line through a specified point not on the line. So, the textbook (it's a college course, a math for elementary teachers) shows a sideways line segment, with a point above it. I have the list of procedures, but I still don't understand how it is constructed. Can you help me? I really appreciate your time and consideration~

 

[Deleted member 4993]

I am having a hard time understanding how to do construction #7 of the basic constructions. It says to contruct a line parallel to a given line through a specified point not on the line. So, the textbook (it's a college course, a math for elementary teachers) shows a sideways line segment, with a point above it. I have the list of procedures, but I still don't understand how it is constructed. Can you help me? I really appreciate your time and consideration~

Youll need to use the parallel line theorem which states

If two parallel lines are transected by a third, the alternate interior angles are the same size.

Draw line from the given point to the given line - this is your third line as referenced above (transecting line).

Now you need to draw line through the given point - making equal angle to the transecting line.