**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.

**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.

**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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