Calculate segment lengths using the postulate AB + BC = AC
Step 1: Identify the Three Points
Determine if point B lies on segment AC between endpoints A and C.
Why: The postulate only applies when B is actually between A and C on the same line.
Step 2: Label Known and Unknown Segments
Know which lengths (AB, BC, or AC) are given and which need to be found.
Why: This determines which algebraic equation you'll solve (addition or subtraction).
Step 3: Write the Equation
Set up AB + BC = AC or rearrange to AB = AC - BC or BC = AC - AB.
Why: The postulate expresses an invariant relationship that must hold for collinear points.
Step 4: Substitute Known Values
Plug in the measured or given lengths into your equation.
Why: Substitution converts the abstract postulate into a concrete calculation.
Step 5: Verify Collinearity
Check that all three lengths are positive and satisfy the addition relationship.
Why: Invalid results indicate that points may not be collinear or data may be inconsistent.
The Segment Addition Postulate states that if a point B lies on a line segment AC, then:
AB + BC = ACThis means the total length of the segment is the sum of its parts.
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