Lines are the most basic shape that we learn about in Geometry. Almost all the shapes are formed when multiple lines come together in particular positions and orientations. In this chapter, we’ll learn all about a pair of lines, their properties and so on.
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Pair of Lines
- Point: A point is an exact location and is represented by a fine dot made by a sharp pen on a sheet of a paper. Thus, A is a point, as shown in the adjoining figure.
- Line: Line is the collection of points which has only length, not breath and thickness. A line is a straight path that is endless in both directions. We denote it by AB or BA. Note that a line has no endpoint.
Browse more Topics under Lines And Angles
- Basics of Geometry
- Parallel Lines and Transversal
- Angles and its Types
- Properties of Angles
- Related Angles
- Interior and Exterior Angles of Triangles
Intersecting Lines
A pair of lines, line segments or rays are intersecting if they have a common point. This common point is their point of intersection. For example, two adjacent sides of a sheet of paper, a ruler, a door, a window and letters.
Parallel Lines
If a pair of lines lie in the same plane and do not intersect when produced on either side, then such lines are parallel to each other.
If L and M are two parallel lines, we read it as L is parallel to M. We know that two lines in the same plane either intersect or are parallel to each other. However, these two lines L and M, lying in the same plane are parallel if they do not meet anywhere, however far they are extended.
Note that the distance between two parallel lines is the same everywhere. For example a railway track, opposite sides of a blackboard, two opposite edges of a door etc.
Transversal Lines
A straight line which cuts two or more straight lines at distinct points is called a transversal line. For example, a railway line crossing several other lines. In the figure, t is a transversal line and l, m are parallel lines.
Let us study Parallel lines and Transversal lines in detail.
Solved Example
Question 1: Give an example of intersecting lines and parallel lines from your surroundings.
Answer :
- Parallel lines: the railway tracks
- Intersecting line: roadways
Question 2: In the adjoining figure-
- Name all the lines present in figure
- Find pairs of intersecting lines
- Find the parallel lines.
Answer :
- Line A, line B, line C, line D
- Line A and line C, line A and line D, line B and line C, line B and line D, line D and line C.
- Line A and line B
Question 3: Prove that distance between two parallel lines is the same everywhere.
Answer : Parallel Lines are lines that never intersect each other. Thus, the distance between them always remains the same.
Question 4: Can two lines intersect at more than one point?
Answer : No, two lines can’t intersect at more than one point.
Question 5: How many transversals can you draw on any two given lines?
Answer : Infinitive
Question 6: If a line is a transversal to 4 lines, at how many points will it intersect them?
Answer : 4 points
Question 7: Is it necessary that a transversal can intersect only parallel lines?
Answer : No, it is not necessary that a transversal can intersect only parallel lines. A transversal can cut any two lines.
Question 8: Which pairs of lines are parallel?
Answer: When the slopes of the two lines are equal then the two lines will be parallel. Moreover, two lines will be perpendicular when their slopes are negative reciprocals of each other. In addition, the slopes of these two equations are the coefficient for the value of x. Thus, both slopes are equal so the lines are parallel.
Question 9: What equation represents a straight line?
Answer: Commonly, the equation of the straight line is y = mx + c, where m is the gradient, and y = c is the value where the line cuts the y-axis. Moreover, we call this number c the intercept on the y-axis.
Question 10: What is a straight line in mathematics?
Answer: It refers to a set of all points between and extending beyond two points. Furthermore, two properties of straight lines in Euclidean geometry are that they have only one dimension, length, and they extend in two directions forever.
Question 11: How to prove that two lines are perpendicular?
Answer: They are perpendicular when their slopes are negative reciprocals. In addition, for finding the slopes, we must put the equation into slope-intercept form, y = mx + c where m equals the slope of the line.
