CONSTRUCTION OF PARALLEL AND PERPENDICULAR LINES
About "Construction of parallel and perpendicular lines"
Construction of parallel and perpendicular lines :
Here, we are going to see, how to construct parallel and perpendicular lines.
Parallel lines :
Parallel lines are the lines which will never intersect and the perpendicular distance between them will be same at everywhere.
Perpendicular lines :
The two lines which have the angle of inclination 90° at the point of intersection are called as perpendicular lines.
To have better understanding on constructing perpendicular lines, let us look at some examples.
Construction of parallel lines - Example
Example :
Using a set square and a ruler draw a line parallel to a given line through a point at a distance of 5cm above it.
Solution :
Step 1 :
(i) Draw a line XY using ruler and mark a point A on it.
(ii) Draw AM = 5cm with the help of a set square.
Step 2 :
Place the set square on the line segment XY.
(i) Place the set scale as shown in the figure.
Step 3 :
(i) Pressing tightly the ruler, slide the set square along the ruler till the edge of the set square touches the point M.
(ii) Through M, draw a line MN along the edge.
(iii) MN is the required line parallel to XY through M.
Construction of perpendicular lines - Examples
Example 1 :
Using a set square and a ruler construct a line perpendicular to given line at a point on it.
Solution :
Step 1 :
(i) Draw a line AB with the help of a ruler.
(ii) Mark a point P on it.
Step 2 :
(i) Place a ruler on the line AB
(ii) Place one edge of a set square containing the right angle along the given line AB as shown in the figure.
Step 3 :
(i) Pressing the ruler tightly with the left hand, slide the set square along the ruler till the edge of the set square touches the point P.
(ii) Through P, draw a line PQ along the edge.
Step 4 :
PQ is the required line perpendicular to AB. Measure and check if m<APQ = m<BPQ = 90°
Example 2 :
Using a set square and a ruler draw a line perpendicular to the given line through a point above it.
Solution :
Step 1 :
(i) Draw a line PQ using a ruler
(ii) Mark a point A above the given line
Step 2 :
(i) Place the ruler on the line PQ
(ii) Place one edge of a set square containing the right angle along the given line PQ as shown in the figure.
Step 3 :
(i) Pressing tightly the ruler with the left hand, slide the set square along the ruler till the edge of the set square touches the point A
(ii) Through A draw a line AO along the edge.
Step 4 :
(i) AO is the required line perpendicular to PQ.
(ii) Measure and check : m<POA = <mQOA = 90°
After having gone through the stuff given above, we hope that the students would have understood "Construction of parallel and perpendicular lines".
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