# Parallel Lines

In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity.

### What are parallel lines in geometry?

Two lines which do not intersect each other at any point even if extended to infinity are called parallel lines.

The lines that always keep the same distance between them are parallel lines. These lines will never meet or intersect each other. There can be more than two lines parallel to each other. We have seen parallel lines on the zebra crossing while crossing the road.

Definition of Parallel Lines:

When two lines do not intersect each other and they have no point in common, they are called parallel lines.

For example:

The opposite edges of a ruler, rail lines, cross-bars of the window, etc. are parallel lines.

Some more examples of parallel lines are shown below.

In the figures given below line AB is parallel to CD and line PQ is parallel to RS.

Thus, two lines are parallel if;

(i) they lie on the same plane.

(ii) they do not have any common point in between.

(iii) the distance between these two lines always remains same everywhere.

Line ℓ and m are parallel are parallel to each other.

The symbol for parallel lines is ||,

therefore, ℓ || m.

Two rays are parallel if the corresponding lines determined by them are parallel.

Two segments are parallel if the corresponding lines determined by them are parallel.

Parallel lines do not meet even if they ere extended indefinitely on the either side. There can be more than two lines parallel to each other.

In figure (i) ℓ is parallel to m. We also write it as ℓ m.

In figure (ii), the lines p and q do not intersect. But on extending these lines, they meet at a point O. So, these are not parallel lines. From our daily life, we can say that the two rails of a railway line, the two edges of a ruler, etc., are examples of 'parallel lines'.

## Working Rules to Draw Parallel Lines:

Step I: Draw two lines ℓ and m in such a way that when these two lines are extended in either direction, they do not meet at any point. There is no common point.

Step II: These lines are parallel lines. We write them as ℓ || m.

## Drawing Parallel Lines with Set Squares:

Draw a line segment through P which is parallel to $$\overleftrightarrow{AB}$$.

Procedure:

Step I: Place one edge of the two smaller edges of any set square along  $$\overleftrightarrow{AB}$$.

Step II: Place the longest edge of the other set square along the free side of the first set square.

Step III: Press the second set square in position and slide the first set square until its edge passes through P. The direction of the slide is shown by an arrow.

Step IV: Draw the line through P with the help of the edge passing through P. While drawing this line, the first set square must be pressed in position.

## Activity:

Step I: Take a rectangular sheet of paper.

Step II: Fold it half so that one part may cover the other part completely.

Step III: Fold it again in the same manner.

Step IV: Now unfold it to get three creases. These creases are parallel to one another.

Solved Problems on Parallel Lines:

 1. In the given figure, find:(i) all the lines with names.(ii) all pairs of parallel lines.Solution:(i) Lines: ℓ, m, n, p(ii) All pairs of parallel lines are     (a) ℓ, m or, ℓ ∥ m     (b) m, n or m ∥ n     (c) ℓ, n or ℓ ∥ n

Worksheet on Parallel Lines:

1. Draw the following:

(i) Draw a line segment AB. Mark a point C above it. Draw a line segment through C parallel to AB.

(ii) Draw a line segment AB of suitable length. Mark a point P above it. Draw PQ perpendicular to AB using set squares.

(iii) Draw a vertical line segment AB. Mark a point H on its right side. Draw a line segment through H parallel to AB.

(iv) Draw a line segment EF. Mark a point G below it. Draw a line segment through G parallel to EF.

## You might like these

• ### 5th Grade Geometry Worksheet | Angles | Triangles | Classification

In 5th Grade Geometry Worksheet we will classify the given angles as acute, right or obtuse angle; using a protractor, find the measure of the given angle, classify the given triangle and circle the numbers with right angles. 1. Write 3 examples of right angles. 2. Name the

• ### Construction of Angles by using Compass, Construction of Angles

In construction of angles by using compass we will learn how to construct different angles with the help of ruler and compass.

• ### Bisecting an Angle | Bisecting an Angle by Using a Protractor | Rules

Bisecting an angle means dividing it into two equal angles. The ray which bisects an angle is known as its bisector. ∠LMN is the given angles. Fold the paper so that LM falls along MN

• ### Construction of an Angle using a Protractor | Drawing an Angle

We will learn how to construction of an angle using a protractor. Let us draw an angle whose measure is 60°. Use a ruler to draw YZ. Now, place the protractor over YZ such that the baseline of the protractor coincides with YZ and midpoint of the baseline coincides with point

• ### Construction of Perpendicular Bisector of a Line Segment|Steps-by-Step

Here we will learn how to construct a perpendicular bisector of a line segment. The perpendicular bisector of a line segment is the line that is perpendicular to the line segment at its mid-point.

• ### Construction of Perpendicular Lines by Using a Protractor, Set-square

Construction of perpendicular lines by using a protractor is discussed here. To construct a perpendicular to a given line l at a given point A on it, we need to follow the given procedure

• ### Types of Three-Dimensional Shapes | 3D Shapes | Definition, Properties

We will learn different types of three-dimensional shapes. Three-dimensional figures are also called solids. The most commonly used solids are cuboids, cylinders, cones and tetrahedrons. A three dimensional shape can be better described, if its faces, edges and vertices

Types of quadrilaterals are discussed here: Parallelogram: A quadrilateral whose opposite sides are parallel and equal is called a parallelogram. Its opposite angles are equal.

• ### Pairs of Angles | Complementary Angles | Supplementary Angles|Adjacent

Pairs of angles are discussed here in this lesson. 1. Complementary Angles: Two angles whose sum is 90° are called complementary angles and one is called the complement of the other.

• ### Classification of Triangle Worksheet | Scalene | Isosceles|Equilateral

In classification of triangle worksheet contains various types of questions on scalene triangle, isosceles triangle, equilateral triangle, acute angled triangle or acute triangle, obtuse angled triangle or obtuse triangle, right angled triangle or right angle.

• ### Medians and Altitudes of a Triangle |Three Altitudes and Three Medians

Here we will discuss about Medians and Altitudes of a Triangle. Median: The straight line joining a vertex of a triangle to the midpoint of the opposite side is called a median. A triangle has three medians. Here XL, YM and ZN are medians. A geometrical property of medians

• ### Pairs of Lines | Parallel and Perpendicular Pairs of Lines | Example

Here we will learn pairs of lines. When pairs of lines are given in a plane, they maybe (i) parallel to each other. (ii) intersecting each other. Two lines in a same plane not intersecting each other are called parallel lines. The lines AB and CD never meet each other

• ### Classification of Triangle | Types of Triangles |Isosceles|Equilateral

Triangles are classified in two ways: (i) On the basis of sides and, (ii) On the basis of angles.In classification of triangle there are six elements in a triangle, that is, three sides and three angles. So, classification of triangle is done on the base of these elements.

• ### Properties of Triangle | Angle Sum Property | Triangle Inequality Prop

We will discuss here about the properties of triangle. Property 1: Relation between the measures of three angles of triangle: Draw three triangles on your not book. Name them as ∆PQR, ∆ABC and ∆LMN.

• ### Worksheet on Angles | Questions on Angles | Homework on Angles

In worksheet on angles you will solve different types of questions on angles. Classify the following angles into acute, obtuse, right and reflex angle: (i) 35° (ii) 185° (iii) 90°

Parallel Lines.

Perpendicular Lines.

Construction of Perpendicular Lines by using a Protractor.

Sum of Angles of a Quadrilateral.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

Sep 15, 24 04:57 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…

2. ### Counting Before, After and Between Numbers up to 10 | Number Counting

Sep 15, 24 04:08 PM

Counting before, after and between numbers up to 10 improves the child’s counting skills.

3. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 15, 24 03:16 PM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

4. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.