Steps to Construct a Parallel Line Through a Point

Now it’s time to take a step further and learn how to construct a parallel through a given point. Make an effort to follow the instructions several times—it’s a good way to practice.

Construction of a Parallel Through Point $P$ (Method 1)

Rule

InstructionsforMethod1

1.
You have a line $l$ and a point $P$ not located on line $l$.
2.
Construct the normal from $P$ to the line $l$. Draw a line from $P$ to $l$, and draw it well past $l$. Call this line $m$.
3.
Now, construct a normal to $m$ at the point $P$.
4.
The normal you constructed in the previous item is the line that’s parallel to $l$ through $P$.

Construction of a Parallel Through Point $P$ (Method 2)

Rule

InstructionsforMethod2

1.
You have a line $l$ and a point $P$ not located on line $l$.
2.
Construct the normal from $P$ to the line. Give the intersection between the line $l$ and the normal the name $B$.
3.
Mark a point $A$ on the line $l$.
4.
Construct a normal at $A$.
5.
Measure the distance from $P$ to $B$ with your draft compass.
6.
Without changing the distance between the legs of your draft compass, put the point on $A$ and make a small arc that intersects with the normal you constructed from $A$. Call this intersection $C$.
7.
Draw the line from $P$ to $C$ with a ruler. This line is the parallel to $l$ through the point $P$.