Therefore, in the above figure, angles 1, 2, 7 and 8 are exterior angles. The angles whose arms do not include the line segment PQ are called exterior angles. we have labelled them 1 to 8 for the sake of convenience and shall now classify them in the following groups – Exterior Angles Let l and m be two lines and let n be the transversal intersecting them at P and Q respectively as shown below –Ĭlearly, lines l and m make eight angles with the transversal n, four at P and four at Q. Now, as we can see in the above figure, a transversal makes some angles with the lines it intersects. Hence, the line p is a transversal to the lines l and m.
For example, in the figure below, the lines l and m are parallel while the line p is intersecting both the line l and the line m. Parallel Lines and Transversalīefore we move to understand how a transversal affects a pair of parallel lines, let us the basic definition of a transversal.Ī transversal is defined as a line intersecting two or more given lines in a plane at different points. Thus the line of zero slope is parallel to the x-axis. This means that either the line is x-axis or it is parallel to the x-axis. Let θ be the angle of inclination of the given line with the positive direction of the x-axis in an anticlockwise sense. What can be said regarding a line is its slope is zero ? Let us now understand the slop using some examples. The angle of inclination of a line with the positive direction of the x-axis in an anticlockwise sense always lies between 0 0 and 180 0. Also, the slope of a line equally inclined with axes is 1 or -1 as it makes an angle of 45 o or 135 o with the x-axis. a line that is perpendicular to the x-axis makes an angle of 90 o with the x-axis, so its slope is tan $\frac$ = ∞. Since a line parallel to the x-axis makes an angle of 0 o with the x-axis, therefore, its slope is tan 0 0 = 0Ī line parallel to the y-axis, i.e. The slope of a line is generally denoted by m. The trigonometrical tangent of the angle that a line makes with the positive direction of the x-axis in an anticlockwise sense is called the slope or the gradient of a line. To find the gradient of a parallel line, let us first recall what we mean by the slope of a line. It should be noted that the slope of any two parallel lines is always the same. The steepness of the line is determined by the slope or the gradient of the lone which is represented by the value m. The Slope Intercept forms of a straight line is given by y = m x + c, where ‘m’ is the slope and ‘c’ is the y-intercept. Equationįor obtaining the equation of parallel lines, let us recall what we mean by the slope intercept form of the equation of a line. For instance, below we have the lines l and m as intersecting lines as they are not parallel. It should be noted that if two lines are not parallel, they will intersect each other. Symbolically, two parallel lines l and m are written as l || m. No matter how much we extend the parallel lines in each direction, they would never meet.This means that parallel lines are always the same distance apart from each other. The distance between a pair of parallel lines always remains the same.The following are the properties of parallel lines – Thus we can define parallel lines as – “Two lines l and m in the same plane are said to be parallel lines of they do not intersect when produced indefinitely in either direction.” Properties There can be many lines in a plane, some of which may intersect each other while some may not intersect when produced in either direction.
Real Life Applications of Parallel Lines.Rules for Parallel Lines Intersected by a Transversal.Alternate Exterior Angles in a Transversal.
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