how do i divide a line into 3 equal parts?

Question

with a compass?

Answer 1

With a compass, you can just resort to trial and error: However, the better way is to draw a line from one end of the line to be divided. Put three divisions on the line drawn, with one section beginning at the end of the intersection. Draw lines from the graduated line to the line to be divided, such that the lines drawn are in parallel to a line passing the end of the graduation and the end of the line to be divided. graduation

Answer 2

It is impossible to divide a line into three equal parts. A line by definition goes on and on in both directions indefinately. You can not divide an infinite object into three equal parts.

If you want to divide a line segment that is a different story.

Set your compass so that it is slightly longer (about 2 inches) than half the line segment. Put the pointy end (the non-drawing end) at one end of the line segment and draw a circle. Put the pointy end at the other end and do it again. Your two circles will intersect in two spots.

Take a ruler and draw a line from one intersection to the other. You should now have a line bisecting your line segment (cutting it in half).

Repeat this process twice more to bisect each half of the line segment. Once you have bisected each half of the line segment you will have divided it into thirds.

Note: you will have to resize your compass so it is slightly longer than half of each new line segment before these last two bisections.

You are finished. May I have 10 points please?

Answer 3

with a ruler draw another line (line b)(any length any angle) from one end of your line (line a). put your compass point on the corner and mark a small arc thru that line b, where the arc intersects line b put your compass point and draw another arc further along and then another. that last point connects up to the other end of line a, now you should have what looks like a triangle, go back to your arced points and draw in lines parallel to the last line of the triangle you drew in, this separates line a into 3 equal parts

Answer 4

Let the given line segment be AB. Draw any acute angle BAX. With compass, mark points A1, A2 and A3 such that:
AA1 = A1A2 = A2A3.

Join A3 and B. Draw lines from A2 and A1 parallel to A3B intersecting AB at P and Q respectively. You will find that AP = PQ = QB. Three equal parts. Done.

Mail me if you have trouble understanding how to draw parallel lines.

Answer 5

you cant..

i think thats what mr euclid did not found out, and included it in a list of things you cant draw using a staight edge and a compass. this includes:
dividing a line segment in to 3 equal parts.
dividing an angle into 3 equal parts.
dividing a square into 2 (as is 2sqaure equal parts)
etc.. man that was my High School Geometry, sorry i cant remember all of them or the exact postulates..

Answer 6

Draw a horizontal line having step of 3 (units). You may use a square line book and mark 9 units on it horizontally. Mark equal 3 distances on this line.

Mark left point of line as 'O'

Draw 'your line' also starting from point 'O'

1) Join end point of 'your line' with end point of line having step of 3 units line

Draw two more parallel lines to line (1) that passes through "points dividing horizontal line into three equal parts.

Said parallel lines cut "your line" equally into three parts!

Answer 7

This is hard to describe without a diagram. Here is a link to an illustrated step by step procedure to divide a line segment into as many equal parts as you want.

http://www.mathopenref.com/constdividesegment.html

Answer 8

Several methods that don't involving parallel lines and marking an additional line with the compass are given at http://www.maa.org/sites/default/files/images/upload_library/23/styer/trisecting/index.html

Answer 9

I found this wonderful Java applet, which shows how to
divide a line into 5 parts, but it's adaptable to any number.

http://www.mathopenref.com/constdividesegment.html

Answer 10

Please kindly preview the video for a guide :)