CONSTRUCTION OF PARALLEL AND PERPENDICULAR LINES

In this section, you will learn 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.

Let us look at some examples to understand how to construct parallel and perpendicular lines.

Example 1 :

Using a set square and a ruler draw a line parallel to a given line through a point at a distance of 5 cm above it.

Solution :

Step 1 :

(i) Draw a line XY using ruler and mark a point A on it.

(ii) Draw AM = 5 cm 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.

Example 2 :

Using a set square and a ruler, draw 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 mAPQ = mBPQ = 90°.

Example 3 :

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 : mPOA = mQOA = 90°.

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