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

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

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

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

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

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

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

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

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

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6 