draw a line ,say AB take a point c outside it.through C draw a line parallel to AB using ruler and compass with steps of construction
Answers
Given a line AB with Point C outside it.
Mark point D on the line AB. Join CD
With D as center, and any radius, draw an arc intersecting AB at E, and CD at F.
With C as center, and same radius as before, draw an arc intersecting CD at G.
Open a compass to length EF
Now,with G as center, and compass opened the same radius as before, draw an arc intersecting the previous arc at H.
Draw a line m passing through C and H.
Thus m is the line parallel to AB, and passing through point C
∴m∣∣AB
Answer:
Step 1
Begin by 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 letters are unimportant except to identify your line.
For our example, we will construct line
L
D
.
Draw a single point above your line, some distance away (like 3 inches) and give it a label.
We will call ours
P
o
i
n
t
U
.
How To Construct Parallel Lines: Step 1
Step 2
Next, we will use our straightedge to construct a transverse, a line intersecting your original line and going through your point above the line. Try to make it at an angle not 90°. This will make your work clearer to you.
Label the intersection of your transverse and your original line with another letter not already used. We will call ours
P
o
i
n
t
E
.
How To Construct Parallel Lines: Step 2
So far, we have line
L
D
intersected by transverse
U
E
.
Step 3
Use 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 distance from the two points on your transverse. In our example, the compass is spread slightly more than halfway between
P
o
i
n
t
U
and
P
o
i
n
t
E
. Put the point 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
E
and
L
D
).
Keep the compass legs the same distance apart and repeat the arc with the compass's sharp point on
P
o
i
n
t
U
. Scribe another arc to look similar to the one you just drew.
How To Construct Parallel Lines: Step 3
Step 4
Lift the compass and do not worry about the distance between the legs. You will put the compass's sharp point on the intersection of the first arc you drew and the transverse. Open or close the compass leg to match the distance from that intersection to the arc's other intersection, where it crosses the horizontal line (
L
D
in our example).
How To Construct Parallel Lines: Step 4
Lift the compass, being careful to keep the legs the same distance apart. Put the point down on the intersection of the second arc and the transverse (
P
o
i
n
t
U
in our example). Swing the pencil leg of the compass to make a tiny mark through that second arc.
How To Construct Parallel Lines: Step 4
Where you swung the compass and passed through the second drawn arc, you have a new point of intersection. Label that point. In our example, we call it
P
o
i
n
t
M
.
Step 5
Use your straightedge to construct a line that passes through the original point above 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
n
t
J
on the left and
P
o
i
n
t
B
on the right.
How To Construct Parallel Lines: Step 5
We have now constructed line
J
B
passing through
P
o
i
n
t
s
U
a
n
d
M
and parallel to line
L
D
(which passes through
P
o
i
n
t
E
)