This is a free lesson from our course in Geometry

 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.
Other useful lessons:
 Point, Line, and Plane Line Segment, Ray, Parallel Lines, Pependicular Lines Classifying Angles
(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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