The Segment Addition Postulate: How To Find Distances And Midpoints On Line Segments In Geometry

Segment Addition Postulate

If A, B, and C are collinear points and B is between A and C, the AB + BC = AC

The Segment Addition Postulate is a concept in geometry that states that given two points A and C on a line segment, the point B lies on the line segment AC if and only if the distance between A and B plus the distance between B and C is equal to the distance between A and C. This means that if we have a line segment AC and we want to find a point B between A and C, we can use the Segment Addition Postulate to find the distance from A to B and the distance from B to C, and then add these distances together to get the distance from A to C.

Mathematically, the Segment Addition Postulate can be written as:

AB + BC = AC

Where A, B, and C are points on a line segment and AB, BC, and AC represent the lengths of the line segments between those points.

One key application of the Segment Addition Postulate is in finding midpoints of line segments. A midpoint is a point on a line segment that divides the segment into two equal parts. Using the Segment Addition Postulate, we can find the coordinates of a midpoint by setting AB and BC equal to each other and solving for the coordinates of B. This gives us the midpoint of the line segment AC, which is halfway between points A and C.

Overall, the Segment Addition Postulate is an essential tool in geometry for finding distances and points on line segments. Mastering this concept is crucial for success in higher-level geometry courses and applications.

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