Segment Addition Postulate
If B is between A and C, then AB+BC=AC
The Segment Addition Postulate is a basic geometric principle that states that if a line segment is divided into two or more smaller segments, then the sum of the smaller segments equals the length of the original segment. This postulate is often used in geometry when working with line segments and their lengths.
Formally, the Segment Addition Postulate can be stated as follows:
For any line segment AB and any point P on that segment, the sum of the lengths of the two smaller line segments AP and PB is equal to the length of the whole segment AB. In other words, if we let AP = x and PB = y, then we have:
AB = AP + PB
AB = x + y
This principle is often used in solving problems related to lengths of line segments, such as finding missing lengths, calculating lengths in geometric proofs, and determining congruence between line segments.
In practice, the Segment Addition Postulate is a simple but important concept in geometry that students should familiarize themselves with early on, as it forms the foundation for many other concepts and procedures that will be covered in later courses.
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