![]() Parallel and Perpendicular Lines WorksheetsįAQs on Parallel and Perpendicular Lines What are Parallel and Perpendicular Lines?.Difference Between Line and Line Segment.Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines.Ĭheck out the following pages related to parallel and perpendicular lines. Negative reciprocal means, if m 1 and m 2 are negative reciprocals of each other, their product will be -1. In this case, the negative reciprocal of -4 is 1/4 and vice versa. For example, if the equations of two lines are given as: y = 1/4x + 3 and y = - 4x + 2, we can see that the slope of one line is the negative reciprocal of the other. This can be expressed mathematically as m 1 × m 2 = -1, where m 1 and m 2 are the slopes of two lines that are perpendicular. The slope of one line is the negative reciprocal of the other line. Perpendicular lines do not have the same slope. Mathematically, this can be expressed as m 1 = m 2, where m 1 and m 2 are the slopes of two lines that are parallel. ![]() For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. Here 'a' represents the slope of the line. The equation of a straight line is represented as y = ax + b which defines the slope and the y-intercept. All perpendicular lines can be termed as intersecting lines, but all intersecting lines cannot be called perpendicular because they need to intersect at right angles.Įquations of Parallel and Perpendicular Lines.Perpendicular lines always intersect at 90°.Parallel lines are always equidistant from each other.Observe the following figure and the properties of parallel and perpendicular lines to identify them and differentiate between them. For example, PQ ⊥ RS means line PQ is perpendicular to line RS. Perpendicular lines are denoted by the symbol ⊥. On the other hand, when two lines intersect each other at an angle of 90°, they are known as perpendicular lines. For example, AB || CD means line AB is parallel to line CD. The symbol || is used to represent parallel lines. They are always the same distance apart and are equidistant lines. If two straight lines lie in the same plane, and if they never intersect each other, they are called parallel lines. What are Parallel and Perpendicular Lines?
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