Segment Addition Postulate

The Segment Addition Postulate states that if B lies between A and C on a line, then the lengths AB and BC sum to AC.

Betweenness: A relation describing when one point lies between two other points on a line. The postulate applies only when B lies between A and C.
Algebraic Geometry Proof: A geometric argument that uses algebraic equations to establish relationships or determine measures. Assigning variables to segment lengths converts the postulate into solvable equations.
Euclidean Geometry: The geometry of points, lines, planes, and figures governed by Euclid's parallel postulate. The postulate belongs to the foundational language of elementary Euclidean geometry.
Three Collinear Points: Three distinct points lying on a single straight line. The postulate's basic configuration places one of these points between the other two.
Line Segment: A part of a line bounded by two endpoints, including every point between them. AB, BC, and AC are the segments whose lengths the postulate relates.
Midpoint: The point on a segment that divides it into two segments of equal length. Applying segment addition to a midpoint gives two equal parts whose sum is the whole.
Ruler Postulate: A geometry postulate assigning real-number coordinates to points on a line so distances are absolute differences. It gives a numerical framework in which segment addition follows from ordered coordinates.
Midpoint Theorem: A theorem connecting the segment joining two triangle side midpoints to the third side. Its midpoint relationships rely on comparing and combining lengths of segments.
Distance: A nonnegative measure of separation between two points. The equation concerns segment lengths, which measure distances between endpoints.
Segment Congruence: A relation stating that two line segments have equal length. Congruent parts can be substituted into the addition equation to find a whole segment.

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