How To Draw A Parallel Line

Download Commodity

Download Article

Parallel lines are lines that are equidistant at all points and would never touch if they went on forever.^[one] Sometimes yous may exist presented with 1 line and demand to create another line parallel to it through a given bespeak. You might exist tempted to simply have a straight edge and draw a line that seems right; however, yous could not be sure that the line you synthetic was technically parallel. Using geometry and a compass, you tin plot boosted points that will ensure the line you construct is truly parallel.

one

Locate the given line and the given point. The point will non be on the given line, and can be above or below it. Label the line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m and the point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .
ii

Draw an arc that intersects the given line at 2 unlike points. To practise this, place the compass tip on point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A . Open up the compass so that it is wide enough to reach across line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): k , and so draw an arc that sweeps across the line at points Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B and Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C .

Advertisement
iii
Draw a small arc opposite the given bespeak. To do this, open up the compass a little wider. Set the compass tip on point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B , and describe an arc that sweeps directly across from bespeak Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .
- If the given point is above the line, you should draw this arc below the line. If the given bespeak is beneath the line, you should describe this arc above the line.
- The arc does non accept to be very long, as long equally office of information technology falls directly nether the given point.
4

Depict a another small arc intersecting the previous one. To practice this, go on the compass set to the same width. Set the compass tip on point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C and draw an arc that intersects the previous small arc. Characterization this point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D
5
Describe a line that connects the given point and the intersection of the two small-scale arcs. Characterization this line line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): n . Line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): n is perpendicular to line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): g through points Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A and Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D .^[ii]
- Remember, a perpendicular line is a line that creates a 90 degree angle.
half-dozen

Draw an arc that intersects the perpendicular line at ii unlike points. To exercise this, place the compass tip on indicate Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A , then draw an arc that sweeps across line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): n at points Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): East and Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): F .
7

Depict a small arc opposite the given point. To do this, open the compass a trivial wider. Set the compass tip on bespeak Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): East , and draw an arc that sweeps directly across from point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .
8

Draw a another small arc intersecting the previous ane. To do this, keep the compass set to the same width. Place the compass tip on point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): F and draw an arc that intersects the previous small arc. Label this bespeak Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): G .
ix

Draw a line connecting the given point to this new point. This line is perpendicular to line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): due north . ^[3] Thus, information technology is parallel to line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m and passes through the given point, signal Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .

Advertising

ane
Locate the given line and the given signal. The point will not be on the given line, and tin be above or beneath it. Recollect of this point as one vertex of a rhomb. Since contrary sides of a rhombus are parallel, by cartoon a rhomb we can construct a parallel line. ^[4]
- If the line and point are not already labeled, you might want to label them to easily go on track of the steps.
- For example, yous might have line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): yard and point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .
2
Draw the 2d vertex of the rhombus. To exercise this, gear up the compass tip on the given signal and draw an arc that intersects the given line at some point. Practise not change the width of the compass.
- It does not affair how broad y'all set up the compass, as long as information technology tin intersect the given line.
- Make sure the arc reaches above the given point and intersects the given line.
- For example, you should set up the compass tip at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A and create an arc that intersects line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): chiliad at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B .
3
Draw the third vertex of the rhombus. Using the same compass width, set the compass tip at the 2nd vertex, and draw an arc that intersects the given line at a new point. Do not change the width of the compass.
- The arc only has to exist long plenty to bear witness where it intersects the given line.
- For instance, you should set up the compass tip at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B and create an arc that intersects line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m at betoken Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C .
4
Draw the quaternary vertex of the rhombus. Using the aforementioned compass width, set the compass at the third vertex, and draw an arc that intersects the starting time arc yous drew (through the 2nd vertex).
- The arc but has to be long enough to show where it intersects the first arc.
- For instance, you should gear up the compass tip at betoken Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C and create an arc that intersects the first arc at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D .
5
Draw a line through the showtime and quaternary vertices of the rhomb. This line volition pass through the given betoken and be parallel to the given line, as the ii lines form two opposite sides of a rhomb.
- For example, a line drawn through betoken Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A and indicate Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D volition be parallel to line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): 1000 .
Advert

ane
Locate the given line and the given point. The point volition not be on the given line, and can exist above or below it.
- If the line and point are not already labeled, you might desire to label them to hands keep track of the steps.
- For example, you might have line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m and point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A .
2
Draw a line through the given point and any point on the given line. This is the transverse line you will use to draw two corresponding angles, which will help you form the parallel line.^[v]
- Ensure that the transverse line extends well beyond the given point.
- For case, you might depict a line through point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A that intersects line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B . The new line segment would be Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): AB .
iii
Ready the compass. Set the compass to a width that is less than half of the line segment you synthetic.
- The verbal width of the compass does non matter, every bit long equally information technology is less than half the width of the line segment.
- For example, yous should set the width of the compass so that information technology is less than one-half the width of line segment Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): AB .
4
Depict the commencement angle. Place the tip of the compass on the point where the transverse line intersects the given line. Depict an arc that intersects the transverse line and the given line. Exercise not change the width of the compass.
- For example, you should gear up the compass at indicate Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): B and describe an arc that intersects line segment Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): AB at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C and line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): m at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D . This creates the angle Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): CBD .
5
Describe an arc. Using the same compass width, place the tip of the compass on the given point. Depict an arc that intersects the transverse line above the given point, extending to just below the given point.
- For example, you should set the compass at bespeak Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A and draw an arc that intersects the transverse line above point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A at point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): P .
6
Ready the compass. Set the width of the compass to the width of the first angle you created.
- For case, the first angle you created was Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): CBD , so prepare the tip of your compass on point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): D extend it to indicate Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): C .
seven
Depict the respective angle. Using the width of the first bending, ready the tip of the compass at the bespeak on the transverse line to a higher place the given point, and draw an arc that intersects the arc you created before.
- For case, you should set the compass tip at betoken Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): P and describe an arc that intersects the previous arc at betoken Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): Q . This gives you angle Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): PAQ , which corresponds to angle Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): CBD .
viii
Draw a line through the given point and the indicate created past the ii intersecting arcs. This line is parallel to the given line through the given point.
- For case, a line cartoon through point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): A and point Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): Q creates line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): f , which is parallel to line Failed to parse (MathML if possible (experimental): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): thou .
Advertisement

Add together New Question

Question

How do I construct a line parallel to a given line if the indicate is from a second given line?

You can use any of the methods described in a higher place. Information technology doesn't matter if the betoken is on another line; technically, every point is on an infinite number of lines, fifty-fifty if no line is shown. Then utilise the given indicate and ignore the second given line.
Question

Why only ane parallel line can be drawn through a given betoken?

This is more a affair of intuition than proof. It's the field of study of Euclid's Parallel Postulate. It's considered an axiom and has been the subject of much controversy for centuries.
Question

This is a little disruptive. Will constructing a 90 degree angle and and then taking the newly synthetic line and constructing some other ninety degree angle help?

Yes, your suggestion volition piece of work. You also may find Method three to be less confusing than the other methods shown. Method 3 is just a variation of the method you're suggesting. Information technology uses an acute angle rather than a right bending.
Question

How would I construct an isosceles triangle whose base is 6 cm and altitude 4 cm?

Use a ruler to draw the 6 cm base of operations. Use the ruler and a compass to construct the perpendicular bisector of the base of operations. Marker a point on the perpendicular bisector 4 cm in either management from the base. Draw lines connecting the 4 cm betoken on the bisector to each end of the base. That's the triangle. (In an isosceles triangle, the altitude to the base is a perpendicular bisector.)
Question

How would I exercise this with a triangle?

Given a prepare square or drafting triangle ABC and a straight line drawn on a slice of newspaper: place any side of the triangle (say, AB) along the given line, and depict another line forth either of the other sides of the triangle (say, BC). Flip the triangle over so that the face that had lain on the paper is now facing up away from the newspaper. Place AB along the second drawn line (BC). Draw a 3rd line along side BC. This third line is parallel to the original line. If these instructions are difficult to follow, just experiment with the triangle, and y'all'll effigy it out.
Question

"Ready the compass to a width that is less than half of the line segment y'all constructed." This should be: "Set the compass to a width that is more than than one-half of the line segment y'all constructed," shouldn't information technology?

Information technology actually doesn't matter. The compass tin be ready at any convenient width, although a longer width makes information technology easier to accurately transfer bending CBD along the transverse to form angle PAQ.
Question

Can you draw a parallel line using a ruler?

Yes. Locate two points on the given line that are apart from each other slightly less than the length of the ruler. Place the ruler perpendicular to the line at the start point. Measure a user-friendly distance from the line, and mark a third point at that distance. Exercise the aforementioned thing at the 2nd point, thus mark a fourth betoken on the same side of and at the same distance from the line. With the ruler draw a line passing through the third and quaternary points. That line will be parallel to the original line.

Ask a Question

200 characters left

Include your e-mail accost to get a message when this question is answered.

Submit

Advertizing

Video

Thank you for submitting a tip for review!

Things Y'all'll Need

Pen or Pencil
Straight border or ruler
Compass

About This Commodity

Commodity Summary X

To construct a line parallel to a given line through a signal, locate the given line and the given signal, labeling the line "thousand" and the point "A." And then, place the tip of a compass on indicate A, and depict a large arc that intersects the line at some point, Without changing the width of the compass, set 1 tip on the intersection betoken, and make another intersection signal forth the line, creating a third vertex for an invisible rhombus. Move the compass so that it's the same width with ane tip on the third vertex, and intersect the showtime arc that you drew. Finally, connect point A to the final vertex of the rhombus to describe the line. For tips on using perpendicular lines and corresponding angles to draw parallel lines, read on!

Did this summary assistance you?

Thanks to all authors for creating a page that has been read 212,791 times.