Segment Addition Postulate Calculator by Omni

Segment Addition Postulate Calculation Chart

Equation: If B is between A and C on a line, then AB + BC = AC

Segment Addition Postulate Formula

Mathematically, it can be expressed as:

AB + BC = AC

Where:

• A, B, and C are points on a line
• B is between A and C
• AB represents the length of the segment from A to B
• BC represents the length of the segment from B to C
• AC represents the total length of the segment from A to C

Example: If AB = 5 units and BC = 3 units, then AC = AB + BC = 5 + 3 = 8 units.

The Segment Addition Postulate states that the length of a line segment is equal to the sum of the lengths of its parts.

Segment Addition Postulate Examples

Two-segment example: Given: MN = 12cm, NO = 8cm
Find: MO
Solution: MO = MN + NO = 12cm + 8cm = 20cm

Three-segment example: Given: PQ = 5m, QR = 3m, RS = 7m
Find: PS
Solution: PS = PQ + QR + RS = 5m + 3m + 7m = 15m

Algebraic example: Given: XY = 2x + 3, YZ = x – 1, XZ = 3x + 5
Prove: XY + YZ = XZ
Solution: (2x + 3) + (x – 1) = 3x + 2 = 3x + 5
Therefore, XY + YZ = XZ.

How to find the segment addition postulate?

To apply the Segment Addition Postulate:

Identify the segments: Locate the points on the line and determine which segments are known and unknown.

Write the equation: Express the total segment length as the sum of its parts.

Substitute known values: Replace known segment lengths with their numerical or algebraic values.

Solve for unknowns: Use algebra to find the length of any unknown segments.

Given a line segment AC with point B between A and C:

• AB = 7 units
• AC = 15 units
• Find BC

Step 1: Identify segments (AB, BC, AC)
Step 2: Write equation: AB + BC = AC
Step 3: Substitute known values: 7 + BC = 15
Step 4: Solve for BC: BC = 15 – 7 = 8 units

The length of segment BC is 8 units.

The Segment Addition Postulate is fundamental in geometry, forming the basis for more complex proofs and calculations involving line segments and distances.

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