Parallel Lines: Definition, Properties with Examples

Parallel Lines Definition

Parallel lines are straight lines that never meet or cross each other, no matter how far they are extended. They always stay the same distance apart and lie on the same flat surface, called a plane. In simple words, the parallel lines definition states that these lines move side by side without ever touching. We often see parallel lines examples in real life, like the edges of a road, railway tracks, or lines on a notebook page. The symbol used to show parallel lines is ‘||’.

In geometry, parallel lines are very different from perpendicular lines. According to the definition of perpendicular lines, they meet each other to form a right angle of 90°. But parallel lines never meet or make any angle with each other. To learn more about the properties of parallel lines and how to find them, along with examples, keep reading.

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Parallel Lines Properties

Parallel lines have some specific features that help you identify them. The following parallel lines properties tell us how these lines behave and how we can check if two lines are really parallel:

• Equal Distance: Parallel lines always stay at the same distance from each other. They never come closer or go farther apart.

• Never Meet: No matter how long you extend them on either side, parallel lines will never meet or cross each other.

• Equal Angles with Transversal: When a line cuts two parallel lines, which is called a transversal, some special angles are formed:

• The corresponding angles are equal.

• The alternate interior angles are equal.

• The alternate exterior angles are equal.

• The consecutive interior angles on the same side of the transversal add up to 180°.

These parallel lines properties help you while solving many geometry problems in mathematics.

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Constructing a Parallel Line

Constructing a parallel line becomes easy if you use a ruler and a compass carefully. It helps you draw one line parallel to another through a given point. Let's understand how to construct a parallel line step-by-step:

Given: A line segment AB and a point P outside the line. Draw a line that passes through point P and is parallel to AB.

Steps for Constructing a Parallel Line:

• Step 1: Take any point X on the line AB and join it with point P using a ruler.

• Step 2: With X as the centre, draw an arc that cuts line AB at point N and line PX at point M.

• Step 3: Now, with P as the centre and the same radius, draw another arc that cuts PX at point Q.

• Step 4: Keep the compass on M and measure the distance between M and N. Then, with Q as the centre, draw an arc with the same distance that cuts the first arc at point R.

• Step 5: Join points P and R using a ruler to create a new line, CD. The new line passing through P, which is CD, is parallel to AB.

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Parallel Lines Examples

After learning about the parallel lines definition and parallel lines properties, it is also important to connect the concept to real life, where there are so many parallel lines examples all around us. Check out some common real-life parallel lines examples here:

Real Life Parallel Lines Examples:

1. Railway Tracks: The two rails on a railway track are parallel because they always stay the same distance apart.

2. Road Lanes: The white lines that divide lanes on a highway or road are parallel to each other.

3. Zebra Crossings: The white stripes you see on a zebra crossing are parallel lines examples.

4. Stair Railings: The two railings on a staircase are also parallel, helping us walk safely.

5. Walls and Buildings: The opposite sides of a wall, window, or rectangular building are parallel.

Geometric Parallel Lines Examples:

6. Rectangle and Square: The opposite sides of rectangles and squares are parallel.

7. Parallelogram: In a parallelogram, both pairs of opposite sides are parallel to each other.

8. Graph Paper Lines: The vertical and horizontal lines on graph paper are parallel lines examples in geometry.

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Are Parallel Lines the Same as Perpendicular Lines?

Parallel lines are not the same as perpendicular lines. Parallel lines always stay the same distance apart from each other and never meet, no matter how long they are extended. They run side by side and never make any angles with each other.

On the other hand, the definition of perpendicular lines tells you that these lines meet or cross each other at a right angle (90°). So while parallel lines never touch, perpendicular lines always intersect to make exact right angles.

Read more: Straight angle 

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