Geometrical Construction
Geometrical construction is all about drawing lines, angles, and different shapes using pen, pencil, straight edge, protractor and a compass. A compass is a geometrical drawing instrument used for drawing circles and arcs. A straightedge, such as a ruler, is used to draw line segments. You can use a compass and a straightedge to construct basic geometric figures. You know a line segment is a line with two endpoints. Line segments that have the same length i.e equal measures are called congruent segments. To draw any shape you should know how to copy line segments.In this article we will study how to copy line segments using pure construction using ruler compass step by step.
Line Segment
A line segment is defined as a part of a line which connects two points within a line. Different numbers of line segments give us different geometrical figures. A line segment is formed by two endpoints. In the figure, m is any line and AB is the line segment on the line m.
[Image will be Uploaded Soon]
Constructing Copy of Line Segment
The tools you will need to copy and construct any line segment of a given length, along with your pen or pencil, are a compass and a straight edge. The most common straight edge is the ruler. But you can use anything that will give you a nice clean straight line. The compass is the mathematical tool that lets you draw nice clean circles and arcs.
The construction of line segments is not accurate when we use a ruler. Hence, we can make use of a ruler-compass combination to construct a copy of line segments. This is the pure construction in maths as no measures and numbers are involved. It is necessary to draw the straight line for the given measure in order to copy it.
Steps for Pure Construction Using Ruler Compass:
PQ is a given line segment whose copy is to be constructed
[Image will be Uploaded Soon]
Step 1: Mark any R that will be one end point of the new segment.
[Image will be Uploaded Soon]
Step 2: Set the compass pointer exactly on the point P of the line segment to be copied
[Image will be Uploaded Soon]
Step 3: Adjust the compass such that the pointer is at P and the pencil point is at Q. The compass width is now equal to the length of the line segment PQ which is to be copied.
[Image will be Uploaded Soon]
Step 4: Without disturbing the compasses' width, place the compass point on the the point R on the line you drew in step 1
[Image will be Uploaded Soon]
Step 5: Without changing the compass width, Draw an arc roughly where the other endpoint of the segment will be.
[Image will be Uploaded Soon]
Step 6: Pick any point say S on the arc that will be the other endpoint of the new line segment.
[Image will be Uploaded Soon]
Step 7 :Draw a line from point R to point S.
[Image will be Uploaded Soon]
Step 8: Thus we get the line segment RS is equal in length to the line segment PQ. RS is the copy of the line segment PQ
[Image will be Uploaded Soon]
Proof:
The compass is considered as a measuring tool for copying the line segment. Since the original line segment and the copied line segment are of the same length, the segments are considered as congruent line segments. Therefore PQ = Rs
All the points on the arc are the same distance from R, as R is the center of the arc.
FAQs on Construction of Copy of Line Segments
1.How to Construct a Perpendicular Bisector?
Answer: A perpendicular bisector is a line that divides another line into two equal parts at a right angle(900).
Here are the steps to constructing a perpendicular bisector of a line.
Set the width of the compass to a little more than half of the given line.The width doesn’t matter so much, as long as it does not change during this step.
Put the pointer of the compass on one endpoint of the line and use the pencil side to draw a small arc on the top and the bottom of the line.
Without changing the width of the compass, repeat this step using the other endpoint of the line.
The arcs should intersect at a point above and a point below the line. Using the ruler, connect these points with a straight line. This is your perpendicular bisector.
[Image will be Uploaded Soon]
2.How to Construct Parallel Lines?
Answer:
Following are the steps to constructing a parallel line.
Draw a point somewhere on your first line that is not directly below the point that you will be drawing the new parallel line. Make the point a good amount to either the left or the right.
Using the straightedge, draw a line connecting your new point and the point for the parallel line. This line is called a transversal.
Using your compass, draw an arc through the first line and the transversal. The pointy part of the compass should be on the point that you created in step 1.
Without changing the width of the compass, draw a similar arc using the point for the new parallel line.
Set the compass width to match where the first arc intersects with the transversal and with the original line.
Don’t change the compass, and move it to the second arc. The pointy part of the compass should be on the intersection of the arc with the transversal and use the pencil part to draw a small arc through the arc that you made in step 5.
Using the straightedge, connect this intersection with the point for your parallel line.
