Segment addition postulate
The Segment Addition Postulate is a fundamental principle in geometry that deals with the addition of two or more segments
The Segment Addition Postulate is a fundamental principle in geometry that deals with the addition of two or more segments. It states that if you have a line segment with three points A, B, and C, then the sum of the lengths of the segments AB and BC will be equal to the length of the entire segment AC.
Mathematically, the Segment Addition Postulate can be represented as:
AB + BC = AC
This postulate holds true for any three points on a line segment, regardless of their order. In other words, it doesn’t matter if point B lies between A and C or if it is on the extension of the line segment. The length of the whole segment remains the same.
To understand this concept better, let’s consider an example. Suppose we have a line segment AB with a length of 6 units and point C lies on the segment such that AC has a length of 3 units. According to the Segment Addition Postulate, the sum of the lengths of AB and BC (which is AC) should also be 6 units.
Mathematically, we have:
AB + BC = AC
6 + BC = 3
To find the length of BC, we can solve the equation:
BC = 3 – 6
BC = -3
However, we cannot have a negative length for a segment. This result indicates that point C is not on the given line segment AB, as the sum of the lengths does not match the length of the entire segment.
The Segment Addition Postulate is a useful tool in geometry as it helps to determine unknown lengths or identify points on a line segment. By knowing the lengths of two segments and the length of the whole segment, we can find missing lengths or determine if a certain point lies on the segment or not.
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