**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 m∠APQ = m∠BPQ = 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 : m∠POA = m∠QOA = 90°.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**