How To construct A Parallel Line v A Point

Step 1

Begin by drawing a heat (or ray or line segment) horizontally on your paper, family member to you. Draw points in ~ each end of her line. Label the clues of her line anything friend like; the letters room unimportant except to identify your line.

You are watching: Construct a parallel line through a point

For ours example, we will certainly construct line LD.

Draw a solitary point above your line, part distance far (like 3 inches) and also give it a label.

We will call ours Point U.


Step 2

Next, us will usage our straightedge to construct a transverse, a heat intersecting your original line and going through your point above the line. Try to do it in ~ an angle not 90°. This will make your job-related clearer come you.

Label the intersection of her transverse and your original line with one more letter not currently used. Us will call ours Point E.


So far, we have actually line LD intersected by transverse UE.

Step 3

Use your compass come scribe one arc. One arc is a ar of a circle. Open up the compass foot so that they are much more than half the distance from the two points on your transverse. In our example, the compass is spread slightly much more than halfway between Point U and Point E. Put the suggest of the compass ~ above Point E and also scribe one arc that goes v the transverse line and also the horizontal line (in ours example, currently UE and LD).

Keep the compass legs the same street apart and also repeat the arc v the compass"s sharp suggest on Point U. Scribe one more arc come look comparable to the one you simply drew.


Step 4

Lift the compass and also do no worry about the distance between the legs. You will put the compass"s sharp suggest on the intersection of the very first arc friend drew and the transverse. Open or nearby the compass leg to match the distance from that intersection to the arc"s other intersection, whereby it the cross the horizontal line (LD in our example).


Lift the compass, being mindful to keep the foot the exact same distance apart. Placed the allude down top top the intersection of the 2nd arc and also the transverse (Point U in ours example). Totter the pencil foot of the compass to make a tiny mark through that 2nd arc.


Where friend swung the compass and also passed through the second drawn arc, you have actually a new point that intersection. Label that point. In ours example, we contact it Point M.

Step 5

Use your straightedge to build a line that passes v the initial point over your very first line and also through the newly labeled point. In our example, that method a line through Point U and Point M.

Put endpoints on that line. Label the endpoints. In ours example, we used Point J ~ above the left and Point B top top the right.


We have actually now built line JB passing with Points U and M and also parallel to heat LD (which passes through Point E). Put it every together, and it might feel JUMBLED yet it yes, really is not!

You have built a heat parallel come your initial line, without measuring anything!

Constructing Parallel Lines

Geometry is manual mathematics. One ability you might need is the capability to construct parallel lines. This will show you how to do it, utilizing the most basic of tools (and no measuring!).

What space Parallel Lines?

Two lines, heat segments, or beam (or any mix of those) are parallel if they never meet and also are constantly the same distance apart. Both lines need to be in the same aircraft (be coplanar).

You conference parallel lines in geometry, that course, but likewise in day-to-day life. The lines of notebook paper are parallel. Political parties of doors, edges of grain boxes, and the floorboards that a residence are parallel.

Classic instances of parallel lines that fool her eye space railroad tracks and also roads, the two lines the which seem to satisfy in the distance. You understand they can not meet, due to the fact that then a train could not relocate or cars could not to the right on the road.

Tools the The Geometrician

A geometrician is a mathematician who research studies geometry. Once you construct figures in geometry, you space a geometer. To construct parallel lines, you need these four an easy tools:

PaperPencilStraightedge (like a ruler or any straight, thin, smooth object)Compass (not the type for direction; the type with two legs, one v a allude and one with a pencil)

A good-quality compass will host the position of that legs together you readjust them. If her compass legs slip, obtain a better compass. Friend are depending upon the foot to stay exactly the same distance apart because that several steps in constructing your parallel lines.

For checking your work, you may want an exact ruler, yet it is not necessary.

Checking your Work

Open her compass to spread the foot so the suggest is on one parallel line and the pencil is on the other. Lift your compass, being cautious not come disturb the legs, and also check everywhere along the 2 lines. If the lines are parallel, the distance will be the same almost everywhere you check.

As a less elegant way to check, you can put a ruler to the distance, so lengthy as you measure perpendicular to the 2 lines.

See more: Which Characteristic Helps Identify Nonfoliated Metamorphic Rocks

Lesson Summary

Using just a pencil, straightedge and also compass, you have now learned how to attract parallel lines. You likewise know what parallel present are, you recognize some examples from actual life, and also you know just how to inspect to check out if your attracted lines space parallel. Girlfriend should additionally be maybe to describe the steps to someone else. Notice you walk not should measure anything! Geometry is a powerful component of mathematics.

Next Lesson:

Parallel Postulate

What friend learned:

After viewing the video, researching the drawings, and reading this text, friend will find out to:

Define parallel linesNotice parallel lines in your worldDraw parallel currently using only a pencil, straightedge and also compassExplain to others how to attract parallel linesCheck your work to ensure your lines room parallel