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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

Instructions for Method 1

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 a point 1

Construction of a Parallel Through Point P (Method 2)

Construction of a parallel through a point 2

Rule

Instructions for Method 2

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.

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