Segment Addition Postulate
The Segment Addition Postulate is a fundamental concept in geometry that states that if you have three points A, B, and C that are collinear (i
The Segment Addition Postulate is a fundamental concept in geometry that states that if you have three points A, B, and C that are collinear (i.e., they lie on the same line), then the length of the line segment AB plus the length of the line segment BC equals the length of the line segment AC.
In mathematical notation, the Segment Addition Postulate can be written as:
AB + BC = AC
This postulate is based on the idea that a line segment is a measurable distance between two points. By adding these distances together, we can find the total length of the entire line segment.
To illustrate this concept, let’s consider an example. Suppose we have a line segment where point A has a coordinate of -3 and point B has a coordinate of 1, and we want to find the length of AB. We can calculate it using the formula for finding the distance between two points in a coordinate system:
AB = |B – A|
AB = |1 – (-3)|
AB = |1 + 3|
AB = |4|
AB = 4
So, in this case, the length of line segment AB is 4.
Now, let’s say we have another point, C, with a coordinate of 5. By applying the Segment Addition Postulate, we can find the length of line segment AC:
AB + BC = AC
4 + BC = 5 – (-3) (substituting values for AB and AC)
4 + BC = 8
BC = 8 – 4
BC = 4
So, in this case, the length of line segment BC is 4. Notice that by adding the lengths of AB and BC, we obtain the length of AC, which is 8.
Overall, the Segment Addition Postulate provides a simple and useful tool for calculating the lengths of line segments when given the lengths of other segments on the same line.
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