In this lesson you’ll learn basic concepts of how to identify congruent
Segments
and to find their midpoint. It is important to know that only a
line segment can have a midpoint. A Line or Ray cannot have midpoint, since
line goes on indefinitely in both directions &
ray has only one end, and
hence no midpoint. Any line or segment that passes through the midpoint of a
line segment bisects (cuts) the line segment.
A point M is called the
midpoint of the segment if and if M is between A and B and AM is equal to MB. The midpoint of a segment divides the segment
into two segments of equal length and these two are
congruent segments
by the definition.
(Continued from above)
Congruence is one of the fundamental concepts and relates to geometric figures having
the same size and shape. Line segments are congruent if they have the same length
i.e. two segments with the same length are called congruent segments. Notice that
they
need not be parallel; can be at any angle or orientation in the plane. In the figure
below;
is congruent to
, and
is congruent to
. The congruence
is represented by
symbol
For example: Given- in the figure below showing congruent segments, M is the midpoint
of
. To find the value
of x, follow the steps:
M is the midpoint: AM = MB
Write the equation with x as variable:
5x – 6 = 3x
Solve above equation for x: 5x - 3x – 6 = 3x - 3x 2x – 6 = 0 x = 3
The value of x is 3, as the final answer.
Remember: the properties of congruence and theorems related to congruent segments
are-
Congruence of segments is reflexive
Congruence of segments is symmetric
Congruence of segments is transitive
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is congruent to
, and
is congruent to
. The congruence
is represented by
symbol
