Two or more lines that lie in the same plane and never intersect each other are known as parallel lines. They are equidistant from each other and have the same slope. Let us learn more about parallel lines, the properties of parallel lines and the angles that are formed when parallel lines are cut by a transversal.
1. What are Parallel Lines? 2. Parallel Lines and Transversal 3. Parallel Lines Properties 4. FAQs on Parallel Lines
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Parallel lines are straight lines that never meet each other no matter how long we extend them. Observe the following figure that shows parallel lines. Line ‘a’ is parallel to line ‘b’, and line ‘p’ is parallel to line ‘q’.
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When any two parallel lines are intersected by another line called a transversal, many pairs of angles are formed. While some angles are congruent (equal), the others are supplementary. Observe the following figure to see parallel lines cut by a transversal. The parallel lines are labeled as L1 and L2 that are cut by a transversal. Eight separate angles have been formed by the two parallel lines and a transversal. Each angle has been labeled using an alphabet.
Given below are the pairs of angles formed by the two parallel lines L1 and L2.
- Corresponding Angles: It should be noted that the pair of corresponding angles are equal in measure. In the given figure, there are four pairs of corresponding angles, that is, ∠a = ∠e, ∠b = ∠f, ∠c = ∠g, and ∠d = ∠h
- Alternate Interior Angles: Alternate interior angles are formed on the inside of two parallel lines that are intersected by a transversal. They are equal in measure. In this figure, ∠c = ∠e, ∠d = ∠f
- Alternate Exterior Angles: Alternate exterior angles are formed on either side of the transversal and they are equal in measure. In this figure, ∠a = ∠g, ∠b = ∠h
- Consecutive Interior Angles: Consecutive interior angles or co-interior angles are formed on the inside of the transversal and they are supplementary. Here, ∠c + ∠f = 180°, and ∠d + ∠e = 180°
- Vertically Opposite Angles: Vertically opposite angles are formed when two straight lines intersect each other and they are equal in measure. Here, ∠a = ∠c, ∠b = ∠d, ∠e = ∠g, ∠f = ∠h
Parallel Lines can be easily identified with the basic properties given below.
- Parallel lines are those straight lines that are always the same distance apart from each other.
- Parallel lines never meet no matter how much they are extended in either directions.
How do you Know if Lines are Parallel?
Apart from the characteristics given above, when any two parallel lines are cut by a transversal, they can be identified by the following properties.
- Any two lines are said to be parallel if the Corresponding angles so formed are equal.
- Any two lines are said to be parallel if the Alternate interior angles so formed are equal.
- Any two lines are said to be parallel if the Alternate exterior angles so formed are equal.
- Any two lines are said to be parallel if the Consecutive interior angles on the same side of the transversal are supplementary.
Parallel Lines Equation
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The equation of a straight line is generally written in the slope-intercept form represented by the equation, y = mx + b, where ‘m’ is the slope and ‘b’ is the y-intercept. The value of ‘m’ determines the slope or gradient and tells us how steep the line is.
It should be noted that the slope of any two parallel lines is always the same. For example, if the slope of a line with the equation y = 4x + 3 is 4. Therefore, any line that is parallel to y = 4x + 3 will have the same slope, that is, 4. Parallel lines have different y-intercepts and have no points in common.
Parallel Lines Symbol
Parallel lines are the lines that never meet each other, no matter how long we extend them. The symbol used to denote parallel lines is ||. For example, AB II PQ indicates that line AB is parallel to line PQ.The symbol that denotes non-parallel lines is ∦.
Parallel Lines Examples in Real Life
A few parallel lines examples in real life are given below:
- Railway tracks
- Zebra crossings
- Staircase and railings
☛ Related links
- Points and Lines
- Intersecting Lines
- Line Segment
- Properties of Parallel Lines
- Parallel and Perpendicular Lines
- Equation of a Line
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