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 + CBSegment 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
- XZ represents the entire line segment
- XY and YZ are the two parts of the segment
- The sum of 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 unitsHow 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 + BC
AC = 8 + 5
AC = 13
Alternatively, if we knew AC = 13 and AB = 8, we could find BC:
13 = 8 + BC
BC = 13 – 8
BC = 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 - YZThis 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 that RQ = 6 units, find PR:
PR = PQ – RQ
PR = 15 – 6
PR = 9 units
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