## Segment Addition Postulate

### The Segment Addition Postulate is a basic concept in geometry that helps us understand how to combine or measure segments

The Segment Addition Postulate is a basic concept in geometry that helps us understand how to combine or measure segments. It states that if you have a line segment with two endpoints, then you can add the lengths of the segments together to find the length of the whole line segment.

Mathematically, the Segment Addition Postulate can be stated as follows:

If point B is between points A and C on a line, then the length of segment AB plus the length of segment BC is equal to the length of segment AC.

In other words, if A, B, and C are collinear points, then AB + BC = AC.

This postulate is based on the concept that a line segment is a straight path between two points. By using the Segment Addition Postulate, we can determine the lengths of line segments by adding the lengths of smaller segments.

For example, if we have a line segment AB with a length of 5 units, and point C is between A and B, such that AC has a length of 2 units, then we can use the Segment Addition Postulate to find the length of BC. We know that AB + BC = AC, so substituting the given lengths, we get 5 + BC = 2. Rearranging the equation, we find that BC = 2 – 5 = -3 units. Since segment lengths cannot be negative, we conclude that this scenario is not possible.

Overall, the Segment Addition Postulate allows us to work with and determine the lengths of line segments in a logical and systematic manner. It is a fundamental concept in geometry that helps build a solid foundation for more advanced geometric principles and proofs.

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