What Are Parallel Lines What Are Parallel Lines We are going to learn more about the topic What are Parallel Lines in this session. We say that if we have two or more lines in the plane, they are said to be parallel, when we find that the two lines are equally apart from each other at all the positions. It means that if we measure the distance between the two lines at any point (the distance is the perpendicular distance between the two lines). Here we can also say that the two lines, as they are at the equal distance at all the point, means that they will not meet to each other. We must remember that parallel lines are those that intersect only in the limit at infinity. It directly means that we imagine that they are meeting at infinite, before infinite at any point, we say they do not meet at all and we cannot see them meeting at any point as we cannot see the place at infinite distance. Thus we come to the conclusion that the pair of parallel line are at equal distance apart and so they do not meet at all. Know More About Random Variables Math.Tutorvista.com
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If we look at the railway track, or at the opposite edges of the door or window, they are at the equal distance from each other at all the points, so we say that opposite edges of the table, door, windows , books etc are all the examples of the pair of parallel lines. If we look at the ruled lines in the note book we write in are the examples of the pair of parallel lines in our daily life. If we have any pair of lines which we want to sees that if they are parallel or not, we say that the pair of lines are parallel if any of the following properties of the parallel lines are satisfied. We say that if there are two lines say l and m and there is the transversal passing through these lines, then we say that the pair of the lines l and m are parallel if : 1.
The pair of corresponding angles formed by the two lines and the transversal is equal.
2. If the pair of interior alternate angles formed by the pair of lines and the transversal are equal 3. If the pair of exterior alternate angles formed by the pair of lines and the transversal are equal. 4. If the pair of interior angles on the same side of the transversal formed by the pair of lines and the transversal is supplementary, which means that the sum of the two angles is 180 degrees? 5. If the pair of exterior angles on the same side of the transversal formed by the pair of lines and the transversal is supplementary, which means that the sum of the two angles is 180 degrees? It means that if the pair of interior or a pair of exterior angles form a linear pair, then we come to the conclusion that the pair of lines are parallel. Learn More Regression Table Math.Tutorvista.com
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Also we can say that if any of the above statement is true, the lines are parallel. Example 1) Determine if y = 3x + 7 and -3x + y = -2 are parallel then graph the equations to check. Given lines are y = 3x + 7 and -3x + y = -2 Slope intercept form of the given lines is y = 3x + 7 --------------------> Slope =3 y = 3x - 2 --------------------> Slope =3 Since the slopes of the above two lines are equal, So the two lines are parallel. Example 2) Determine if y =2x - 5 and -7x + y = 4 are parallel then graph the equations to check. Given lines are y =2x - 5 and -7x + y = 4 Slope intercept form of the given lines is y =2x - 5-----------------> Slope =2 y =7x + 4-----------------> Slope =7 Since the slopes of the above two lines are not equal, So the two lines are not parallel.
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