If B is between A and C, then AB+BC=AC.
The statement “If B is between A and C, then AB + BC = AC” represents a mathematical property known as the segment addition postulate
The statement “If B is between A and C, then AB + BC = AC” represents a mathematical property known as the segment addition postulate. This postulate is a fundamental concept in geometry that states that if three points A, B, and C are collinear (meaning they lie on the same line) and B is between A and C, then the sum of the lengths of the segments AB and BC is equal to the length of segment AC.
To understand this property, consider a number line. Let A be the leftmost point, B be a point between A and C, and C be the rightmost point. The distance between A and B can be represented as AB, and the distance between B and C can be represented as BC. According to the segment addition postulate, the total distance from A to C (AC) is equal to the sum of the distances AB and BC.
The segment addition postulate holds true regardless of the specific lengths of AX, BX, and CX, as long as B lies between A and C on the same line. This property is often used in geometric proofs and helps establish relationships between line segments.
For example, if AB = 3 units and BC = 5 units, the sum AB + BC would equal 8 units. In this case, the total length of AC would also be 8 units. However, if the given values of AB and BC were different, the sum AB + BC and the length of AC would still be equal as long as B remains between A and C.
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