How To Construct Parallel Lines Using A Drawing Program

How To Construct A Parallel Line Through A Betoken

Stride 1

Begin past drawing a line (or ray or line segment) horizontally on your paper, relative to you. Draw points at each end of your line. Label the points of your line anything you like; the messages are unimportant except to place your line.

For our case, we will construct line $L D$ .

Draw a unmarried point in a higher place your line, some distance abroad (like three inches) and give it a characterization.

We will telephone call ours $P o i north t U$ .

$How To Construct Parallel Lines: Step 1$

Step 2

Next, nosotros will use our straightedge to construct a transverse, a line intersecting your original line and going through your point above the line. Effort to go far at an angle non xc°. This will make your work clearer to you lot.

Label the intersection of your transverse and your original line with another alphabetic character not already used. We will call ours $P o i n t Eastward$ .

$How To Construct Parallel Lines: Step 2$

And then far, we have line $L D$ intersected by transverse $U E$ .

Footstep 3

Apply your compass to scribe an arc. An arc is a section of a circle. Open the compass legs so that they are more than half the altitude from the two points on your transverse. In our example, the compass is spread slightly more than halfway between $P o i due north t U$ and $P o i due north t E$ . Put the indicate of the compass on $P o i n t E$ and scribe an arc that goes through the transverse line and the horizontal line (in our example, lines $U East$ and $L D$ ).

Keep the compass legs the same distance apart and repeat the arc with the compass's precipitous point on $P o i northward t U$ . Scribe another arc to look similar to the 1 you simply drew.

$How To Construct Parallel Lines: Step 3$

Pace iv

Lift the compass and exercise non worry about the distance between the legs. You will put the compass'due south abrupt signal on the intersection of the starting time arc yous drew and the transverse. Open or shut the compass leg to match the distance from that intersection to the arc'south other intersection, where information technology crosses the horizontal line ( $50 D$ in our example).

$How To Construct Parallel Lines: Step 4$

Lift the compass, being conscientious to keep the legs the same distance apart. Put the point downward on the intersection of the 2d arc and the transverse ( $P o i n t U$ in our case). Swing the pencil leg of the compass to brand a tiny mark through that 2d arc.

$How To Construct Parallel Lines: Step 4$

Where you swung the compass and passed through the second fatigued arc, you accept a new point of intersection. Label that point. In our example, we call it $P o i due north t M$ .

Stride five

Use your straightedge to construct a line that passes through the original signal to a higher place your first line and through the newly labeled point. In our example, that means a line through $P o i n t U$ and $P o i n t M$ .

Put endpoints on that line. Label the endpoints. In our example, we used $P o i north t J$ on the left and $P o i n t B$ on the right.

$How To Construct Parallel Lines: Step 5$

We accept now constructed line $J B$ passing through $P o i n t southward U a n d Chiliad$ and parallel to line $L D$ (which passes through $P o i n t E$ ). Put information technology all together, and information technology may experience JUMBLED but it really is not!

You have synthetic a line parallel to your original line, without measuring anything!

Constructing Parallel Lines

Geometry is hands-on mathematics. One skill you may demand is the ability to construct parallel lines. This will show you how to practise it, using the simplest of tools (and no measuring!).

What are Parallel Lines?

Two lines, line segments, or rays (or whatever combination of those) are parallel if they never meet and are always the same distance apart. Both lines accept to be in the same plane (be coplanar).

You encounter parallel lines in geometry, of grade, but also in everyday life. The lines of notebook paper are parallel. Sides of doors, edges of cereal boxes, and the floorboards of a home are parallel.

Archetype examples of parallel lines that fool your eye are railroad tracks and roads, the two lines of which seem to meet in the distance. You know they cannot meet, because then a railroad train could not move or cars could not fit on the road.

Tools of The Geometrician

A geometrician is a mathematician who studies geometry. When you construct figures in geometry, you are a geometer. To construct parallel lines, you need these four uncomplicated tools:

Paper
Pencil
Straightedge (like a ruler or any straight, sparse, smooth object)
Compass (not the kind for management; the kind with two legs, one with a point and one with a pencil)

A good-quality compass will hold the position of its legs as you conform them. If your compass legs skid, become a better compass. You are depending on the legs to stay exactly the same distance apart for several steps in amalgam your parallel lines.

For checking your work, you may desire an accurate ruler, only it is not necessary.

Checking Your Work

Open your compass to spread the legs and so the indicate is on one parallel line and the pencil is on the other. Lift your compass, beingness careful not to disturb the legs, and check anywhere along the two lines. If the lines are parallel, the distance will exist the same anywhere you lot check.

As a less elegant fashion to check, you tin can put a ruler to the distance, so long as you measure perpendicular to the two lines.

Lesson Summary

Using only a pencil, straightedge and compass, yous have now learned how to describe parallel lines. You too know what parallel lines are, you know some examples from real life, and you know how to check to come across if your fatigued lines are parallel. You should also be able to explain the steps to someone else. Detect you lot did not need to measure anything! Geometry is a powerful function of mathematics.