We’ve created this **segment addition postulate calculator** in geometry to help students solve problems related to **line segments**.

**For example, imagine a line segment AB with a point C between A and B. The postulate asserts that:**

**AB = AC + CB**

## Segment Addition Postulate Calculator

Total Segment | Part 1 | Part 2 | Calculation |
---|---|---|---|

AB = 20 | AC = 8 | CB = ? | CB = AB – AC = 20 – 8 = 12 |

XY = ? | XZ = 15 | ZY = 7 | XY = XZ + ZY = 15 + 7 = 22 |

MN = 30 | MP = ? | PN = 18 | MP = MN – PN = 30 – 18 = 12 |

RS = 25 | RT = 10 | TS = ? | TS = RS – RT = 25 – 10 = 15 |

EF = ? | EG = 5 | GF = 9 | EF = EG + GF = 5 + 9 = 14 |

CD = 40 | CE = 15 | ED = ? | ED = CD – CE = 40 – 15 = 25 |

GH = ? | GI = 12 | IH = 10 | GH = GI + IH = 12 + 10 = 22 |

JK = 50 | JL = 20 | LK = ? | LK = JK – JL = 50 – 20 = 30 |

PQ = 100 | PR = 30 | RQ = ? | RQ = PQ – PR = 100 – 30 = 70 |

XY = 60 | XZ = ? | ZY = 25 | XZ = XY – ZY = 60 – 25 = 35 |

AB = 45 | AC = 15 | CB = ? | CB = AB – AC = 45 – 15 = 30 |

MN = ? | MP = 22 | PN = 10 | MN = MP + PN = 22 + 10 = 32 |

ST = 80 | SU = 50 | UT = ? | UT = ST – SU = 80 – 50 = 30 |

WX = ? | WY = 5 | XY = 25 | WX = WY + XY = 5 + 25 = 30 |

QR = 90 | QS = 45 | SR = ? | SR = QR – QS = 90 – 45 = 45 |

## Segment Addition Postulate Formula

**If X, Y, and Z are collinear points, and Y is between X and Z, then:**

**XZ = XY + YZ**

XZrepresents theentire line segmentXYandYZare thetwo partsof the segment- The
sumof XY and YZ equals XZ

**This formula can be applied to various scenarios:**

**Finding the total length**: If you know the lengths of XY and YZ, you can easily calculate XZ.

**Determining a missing part**: If you know XZ and one of the parts (XY or YZ), you can find the other part.

Suppose **XY = 5 units** and **YZ = 7 units**.

Using the formula:

**XZ = XY + YZ** **XZ = 5 + 7** **XZ = 12 units**

## How to Find Segment Addition Postulate?

**Identify the segments**: Determine which points are**collinear**and which point lies**between**the other two.**Gather known information**: Note the**lengths**of any segments you already know.**Apply the formula**: Use**XZ = XY + YZ**, substituting known values.**Solve for the unknown**: Depending on what you’re looking for,**rearrange**the equation as needed.

Let’s say we have points A, B, and C on a line, with B between A and C. We know that **AB = 8** and **BC = 5**. To find **AC**:

AC = AB + BCAC = 8 + 5AC = 13

Alternatively, if we knew **AC = 13** and **AB = 8**, we could find **BC**:

13 = 8 + BCBC = 13 – 8BC = 5

## What is the Segment Subtraction Postulate in Geometry?

The **Segment Subtraction Postulate** is closely related to the **Addition Postulate**. It states that if a point lies on a line segment, the **difference** of the distances from the endpoints to this point equals the **length** of the remaining segment.

**Mathematically, for collinear points X, Y, and Z, with Y between X and Z:**

**XY = XZ - YZ**

This postulate is particularly useful when you need to find the **length** of a part of a segment when you know the **total length** and one of the parts.

Given a line segment

PQ = 15 units, with point R on PQ such thatRQ = 6 units, findPR:

PR = PQ – RQPR = 15 – 6PR = 9 units

**Related Tools:**