## Segment Addition Postulate

### The Segment Addition Postulate is a fundamental concept in geometry that states that if you have a line segment with three points on it, then the sum of the lengths of the two smaller segments will always be equal to the length of the entire segment

The Segment Addition Postulate is a fundamental concept in geometry that states that if you have a line segment with three points on it, then the sum of the lengths of the two smaller segments will always be equal to the length of the entire segment.

In other words, if you have a line segment AB and there is a point C on the line segment, then AC + CB will always be equal to the length of AB.

To understand this postulate better, let’s consider an example:

Let’s say we have a line segment AB with a length of 10 units. We want to find the length of segment AC, if point C divides AB into two segments, with AC having a length of 4 units.

According to the Segment Addition Postulate, the sum of the two smaller segments, AC and CB, should equal the length of the entire segment AB.

So, if AC = 4 units, and AB = 10 units, we can substitute these values into the equation:

AC + CB = AB

4 units + CB = 10 units

We can now solve for CB by subtracting 4 units from both sides of the equation:

CB = 10 units – 4 units

CB = 6 units

Therefore, the length of segment CB is 6 units.

To summarize, the Segment Addition Postulate is a mathematical rule that states that for any line segment with three points, the sum of the lengths of the two smaller segments will always be equal to the length of the entire segment. This concept is important in geometry and helps us understand relationships between different segments on a line.

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