In this lesson you’ll learn the concepts of Ray, Line Segment, Parallel and
Perpendicular lines & their important properties/usages in Geometry. It is described in the presentation
by instructor using video and with the help of several examples with solution.
A
ray is a part of line that consists of a point on the line called an endpoint and all
other points on one side of the endpoint. It is represented by:
A line segment is a ‘straight’ line that you might draw using the ruler on a piece of paper.
A
line segment does not extend infinitely, but has two designated endpoints.
The terms ‘segment’ and ‘straight line segment’ are also used to refer a line
segment.
Its length is a measure of its size and is the same as the distance between its endpoints.
(More text below video...)
(Continued from above) The line segment AB is represented as
. There are
no arrow heads on the line over AB as in case of a line or ray. E.g. the following
is a diagram of line segment AB:
Two or more lines are called parallel lines if and only if the lines lie in the
same plane but do not intersect. Also they have same slope. All vertical lines are
parallel. When two lines are parallel, they have no points in common. The symbol
used for parallel lines to each other is
. E.g. Line AB is parallel to CD is represented by ABCD, as shown below:
Perpendicular lines are lines that intersect to form a right or 90 degree angle.
If two lines are perpendicular to each other, then the product of their slopes is
equal to – 1.The figure below shows, the lines AB and CD are perpendicular to each
other.
Further on you’ll learn to find if the lines are parallel or perpendicular in the
given case and their properties. For example: to find the number of points of intersection
for one pair of perpendicular lines, you may follow the steps given below:
• two lines are perpendicular intersect at right angles.
• any two perpendicular Lines intersect at exactly one point, is the final answer.
Remember:
• In a plane; if a line is perpendicular to one of two parallel lines, it is perpendicular
to the other line as well
• in a plane; if a line is parallel to one of two parallel lines, it is parallel
to both parallel lines.
• in a plane; if three or more parallel lines are intersected by two or more transversals,
then they divide the transversals proportionally.
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