Two or more lines that lie in the same plane and never intersect are calledparallel lines. They are equidistant from each other and have the same slope. Let's learn more about parallel lines in this article.
|1.||What are parallel lines?|
|2.||Parallel and crossed lines|
|3.||Properties of parallel lines|
|4.||Parallel lines FAQ|
What are parallel lines?
Parallel lines are straight lines that never meet, no matter how far we extend them. Look at the figure below, which shows parallel lines. Line 'a' is parallel to line 'b' and line 'p' is parallel to line 'q'.
Parallel and crossed lines
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), others are complementary. Refer to the figure below to see the parallel lines labeled L1 and L2 crossed by ahe wants. Eight separate angles were formed by the two parallel lines and a transverse line. Each angle was labeled with an alphabet.
Below are the pairs of angles formed by the two parallel lines L1 and L2.
- Corresponding angles: It should be noted that the pair ofcorresponding anglesare the same size. In the given map there are four pairs of corresponding angles, i.e. ∠a = ∠e, ∠b = ∠f, ∠c = ∠g and ∠d = ∠h
- Alternative interior angles:alternate interior anglesare formed in the interior of two parallel lines intersected by a transversal. They are the same size. In this mapping, ∠c = ∠e, ∠d = ∠f
- Alternative outside angles:Alternate Outside Anglesare formed on both sides of the transversal and are equal in size. In this figure, ∠a = ∠g, ∠b = ∠h
- Consecutive interior angles:Consecutive Interior Anglesor co-interior angles are formed within the transversal and are complementary. Here ∠c + ∠f = 180° and ∠d + ∠e = 180°
- Vertically opposite angles:vertically opposite anglesthey arise when two straight lines intersect and are the same size. Here ∠a = ∠c, ∠b = ∠d, ∠e = ∠g, ∠f = ∠h
Properties of parallel lines
Parallel lines can be easily identified using the basic properties given below.
- Parallel lines are straight lines that are always the same distance apart.
- Parallel lines never meet, no matter how far they extend in any direction.
How do you know if the lines are parallel?
In addition to the properties given above, any two parallel lines intersected by a transversal can be identified by the following properties.
- Any two straight lines are said to be parallel if the corresponding angles formed in this way are equal.
- Any two straight lines are said to be parallel if the alternate interior angles thus formed are equal.
- Any two lines are said to be parallel if the alternate exterior angles thus formed are equal.
- Any two lines are said to be parallel if the consecutive interior angles on the same side of the transversal are complementary.
Equation for parallel lines
The equation of astraight lineis usually 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 'm' value determines the slope or slope and tells us how steep the line is.
It should be noted that the slope of 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 parallel to y = 4x + 3 has the same slope, i.e. 4. Parallel lines have differenty interceptsand have no points in common.
parallel lines icon
Parallel lines are the lines that never meet, no matter how long we stretch them out. The symbol used to denote parallel lines is||. For example,ABIIPQshow this lineABis parallel to the linePQ. The symbol that indicates non-parallel lines is∦.
☛ Related Links
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Parallel lines FAQ
What are parallel lines in geometry?
parallel linesare those lines that are always at the same distance and never meet. The symbol used to denote parallel lines is||. For example AB||CD means that the AB line is parallel to the CD line.
What are parallel lines and perpendicular lines?
Parallel lines are lines that are equidistant from each other and never meet, no matter how far they extend in either direction. For example, opposite sides of a rectangle represent parallel lines. On the other hand, if any two straight lines intersect at an angle of 90°, they are calledvertical lines. For example, adjacent sides of a rectangle are perpendicular because they intersect at a 90° angle.
What are the types of angles in parallel lines?
When any two parallel lines are intersected by a transversal, they form many pairs of angles, ascorresponding angles, Alternating interior angles, alternating exterior angles, and consecutive interior angles.
What happens when parallel lines are intersected by a transversal?
When any two parallel lines are intersected by a transversal, the following angles are formed.
- Corresponding angles that are equal.
- Alternate interior angles of the same measure.
- Alternate Outside Angleswhich are the same.
- Consecutive Interior Anglesthat are complementary.
How are the parallel lines?
Parallel lines look like train tracks that never meet and are always the same distance apart. Opposite sides of a rectangle also represent parallel lines that are equidistant.
What is the slope of parallel lines?
If two lines are parallel, they have the same thingTilt. For example, if the equation of a line is y = 1/2x + 17, then its slope is 1/2. Now if a line on the same plane has the same slope of 1/2 then it is parallel to the given line.
What are real examples of parallel lines?
Real-world examples of parallel lines include train tracks, sidewalk edges, rails on a staircase, endless rails, opposite sides of a ruler, opposite edges of a pencil, eraser, etc.
What is the rule for parallel lines?
The rule for parallel lines is that the lines must not meet. In other words, if two lines in the same plane are equidistant from each other and never meet, they are called parallel lines.
What is the symbol for parallel lines?
The symbol used to denote parallel lines is ||. Any two parallel lines AB and CD are represented as AB||CD.
Do parallel lines meet at infinity?
No, the definition itself suggests that parallel lines never meet. Therefore, parallel lines would not meet even at infinity.
Do parallel lines have the same equation?
No, parallel lines don't have the same equation, but they do have the same slope. For example, if the equation of a line is represented as y = 4x + 2, that means that the slope of that line is 4. Therefore, another straight line in the same plane that has the same slope of 4 is parallel to the given line.
Are parallel lines the same length?
No, the parallel lines may not be the same length, but they must be equidistant from each other.
Does a triangle have parallel lines?
nobodytriangleit has no parallel lines. As a triangle always has 3 intersecting sides; and we know that parallel lines never intersect, so a triangle cannot have parallel lines.
How many parallel lines does a hexagon have?
AHexagonis a six-sided polygon. A regular hexagon has three pairs of parallel lines.