Segment Addition Postulate Calculator

Segment Addition Calculator

Calculate segment lengths using the postulate AB + BC = AC

How To Use Segment Addition

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.

Detailed Example

Scenario: On a line, point B divides segment AC. Given AB = 7 cm and BC = 5 cm, find AC.
Step 1 - Identify Points: A, B, C are collinear with B between A and C.
Step 2 - Label Segments: AB = 7 cm (known), BC = 5 cm (known), AC = ? (unknown).
Step 3 - Write Equation: AB + BC = AC, so 7 + 5 = AC.
Step 4 - Substitute Values: AC = 7 + 5 = 12 cm.
Step 5 - Verify: Check: 7 + 5 = 12 ✓ All values positive ✓ Relationship satisfied ✓
Verification: AC (12) = AB (7) + BC (5) confirms the postulate.
Result: The total segment AC is 12 cm long.
Interpretation: Point B divides AC into parts that sum to the whole; this fundamental property applies to all collinear points.

Postulate Information

The Segment Addition Postulate states that if a point B lies on a line segment AC, then:

AB + BC = AC

This means the total length of the segment is the sum of its parts.

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