Perpendicular Lines Definition
Perpendicular Lines Definition
Definition of Parallel and Perpendicular Lines
Parallel Lines are distinct lines lying in the same plane and they never intersect each other.
Parallel lines have the same slope.
In the figure below, lines PQ and RS are paral el and the lines l and m are paral el.
Perpendicular lines are lines that intersect at right angles. If two lines are perpendicular to
each other, then the product of their slopes is equal to - 1.
In the figure shown below, the lines AB and EF are perpendicular to each other.
In geometry, two lines or planes (or a line and a plane) are considered perpendicular (or
orthogonal) to each other if they form congruent adjacent angles (a T-shape).
The term may be used as a noun or adjective. Thus, as illustrated, the line AB is the
perpendicular to CD through the point B.
By definition, a line is infinitely long, and strictly speaking AB and CD in this example
represent line segments of two infinitely long lines.
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Hence the line segment AB does not have to intersect line segment CD to be considered
perpendicular lines, because if the line segments are extended out to infinity, they would still
form congruent adjacent angles.
If a line is perpendicular to another as shown, al of the angles created by their intersection are
called right angles (right angles measure /2 radians, or 90). Conversely, any lines that meet
to form right angles are perpendicular.
In a coordinate plane, perpendicular lines have opposite reciprocal slopes, which means that
the product of their slopes is -1.
A horizontal line has slope equal to zero while the slope of a vertical line is described as
undefined or sometimes infinity. Two lines that are perpendicular would be denoted as
ABCD.
A line can be defined as a geometrical object which is straight, infinitely long and infinitely thin.
About lines one interesting thing is that a straight line is the shortest distance between any two
points. If a line is not straight then generally it is referred as a curve or an arc.
Perpendicular refers to the 90 degrees. Two lines are said to be perpendicular or orthogonal
to each other if they form T-shape angles. Two lines wil be parallel if they remain apart the
same distance (equidistant) to each other and wil not meet ever.
The difference between a parallel and a perpendicular line is a right angle for example if a
Perpendicular Lines Definition is rotated by the 90 degree angle then it would become paral el
(the condition is they should not be in touch to each other). The same definition applied to
paral el curves or surfaces i.e. they should be equidistant to each other always.
In Coordinate Geometry two lines are perpendicular to each other the slope of one line is the
negative reciprocal to other one means they have a reciprocal relationship with each other.
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For example if the slope of one line is m then the slope of the other line would be the negative
reciprocal to m i.e. -1/m. It doesn't matter that from which line we are going to start with
because the equation works in both ways.
The term perpendicular can be replaced with the term normal or orthogonal. If two lines are
perpendicular to each other then it can said that both lines are normal to each other.
It's possible to draw a perpendicular to a line at a point on the line:
Step 1- With the compass on a predefined point (let it be M) set it to a medium width.
Step 2- Draw an arc on each side of the point M using that compass width and create the
other points A and B.
Step 3- With the compass on A; set its width to about half way between M and B.
Step 4- Now draw an arc on one side of the line.
Step 5- Now repeat the same process without changing the width of the compass from
another point B that would create a new point named C.
Step 6- Draw a line from M to C.
Step 7- The line MC is perpendicular to AB at point M.
This process also gives the two same size or congruent triangles if we draw two lines from A
and B to the point C.
The method described below is for constructing a line perpendicular to the given line:


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