Postulate 2.7
Postulate 2.7
Postulate 2.7, also known as the Segment Addition Postulate, is a fundamental concept in geometry. It states that if three points A, B, and C are collinear (lie on the same line), then the distance between A and C is the sum of the distances between A and B, and B and C.
Mathematically, the statement can be written as:
AC = AB + BC
This postulate essentially says that a line segment can be divided into multiple smaller segments, and the total length of the line segment is equal to the sum of the lengths of these smaller segments.
For example, if A, B, and C are three points on a line and the distance between A and B is 5 units, and the distance between B and C is 3 units, then the distance between A and C would be 8 units. This is because 5 + 3 = 8.
The Segment Addition Postulate is a crucial tool used in geometric proofs and calculations. It allows us to break down a line segment into smaller parts and understand their relationship in terms of length.
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