Senast uppdaterad: 19 augusti 2026
Kalkylator för segmentadditionspostulatet
Skapare
Dharmendra SinghGranskare
Skapare
Dharmendra SinghGranskare
Quick Answer
The segment addition postulate states that if B lies between A and C on a line, then AB + BC = AC. This calculator solves for a missing segment length or verifies whether three given lengths satisfy that relationship, while showing the left side, right side, and their difference.
The Segment Addition Postulate Calculator uses AB plus BC equals AC to solve for a missing part or verify whether three segment lengths match a straight-line diagram.
Viktiga Punkter
- The postulate requires collinear points with B between A and C.
- AB and BC are the parts, while AC is the whole.
- Missing lengths come from simple rearrangements of AB + BC = AC.
- Verification mode compares the sum of the parts directly with the whole.
- Most errors come from point-order confusion, not from arithmetic.
Skapare
Dharmendra SinghGranskare
Skapare
Dharmendra SinghGranskare
Formel
AB + BC = AC
Där:
- AB=Length from A to B(units)
- BC=Length from B to C(units)
- AC=Length from A to C(units)
Lösta exempel
Solve for AC
Given AB = 5 and BC = 7, find AC.
- 1Apply the segment addition postulate AB + BC = AC.
- 2Substitute the known lengths: 5 + 7 = AC.
- 3Add the segments to get AC = 12.
Solve for AB
Given AC = 15 and BC = 6, find AB.
- 1Start with AB + BC = AC.
- 2Substitute the known values: AB + 6 = 15.
- 3Subtract 6 from both sides to get AB = 9.
Verify a relationship fails
Check whether AB = 4, BC = 3, and AC = 8 satisfy the postulate.
- 1Compute the left side AB + BC = 4 + 3 = 7.
- 2Compare the sum 7 with the whole segment AC = 8.
- 3Because 7 does not equal 8, the postulate is not satisfied for these lengths.
Introduktion
The Segment Addition Postulate Calculator works with one of the simplest but most important ideas in elementary geometry: if points A, B, and C are collinear and B lies between A and C, then AB + BC = AC. That relationship lets you solve for a missing segment length or verify whether three claimed lengths are consistent with a straight-line diagram. The calculation itself is basic addition or subtraction, but the setup matters. You must interpret which segment is the whole, which two are parts, and whether the point order really matches the postulate. This page therefore supports both solving and verification so users can move from diagrams to algebra and back again without mixing up the pieces.
What the segment addition postulate says
The postulate states that when point B lies between A and C on the same line, the whole segment AC is exactly the sum of the smaller segments AB and BC. This is one of the earliest geometry relationships students use because it turns a diagram into a simple equation. Even so, the meaning of 'between' and 'collinear' is essential; without those conditions, the equation may not apply.
A, B, and C must lie on one line.
B must be between A and C.
AB and BC are the parts.
AC is the whole.
Why AB + BC = AC works
If B sits between A and C on a straight segment, traveling from A to C is the same as traveling from A to B and then from B to C. Length therefore adds naturally. This makes the equation both a geometric fact and an algebra tool. Once written as AB + BC = AC, the relationship can be rearranged to solve for any one missing length as long as the whole segment is at least as long as either part.
Solve for AC by adding the parts.
Solve for AB by subtracting BC from AC.
Solve for BC by subtracting AB from AC.
Verification compares the sum of parts with the whole.
How to read a diagram correctly
Many wrong answers happen because the equation is right but the point order is wrong. A textbook may label the points left to right as A, C, B, or it may place B elsewhere entirely. The postulate only applies in the form AB + BC = AC when B lies between A and C. This calculator assumes that exact arrangement, which is why the labels are fixed and the explanation keeps repeating the point order.
Identify the whole segment first.
Check which point lies in the middle.
Confirm that all three points are collinear.
Translate the picture into AB + BC = AC before calculating.
Worked example: solve for AB
Suppose AC = 15 and BC = 6. Since B lies between A and C, the postulate says AB + BC = AC. Substitute the known values to get AB + 6 = 15. Subtract 6 from both sides, and the missing segment is AB = 9. This is a useful example because it shows the whole-minus-part pattern that appears in many geometry worksheets.
Write AB + BC = AC.
Substitute AB + 6 = 15.
Rearrange to AB = 15 - 6.
Compute AB = 9.
Why verification mode matters
Not every problem asks for a missing value. Sometimes the real question is whether three given lengths can belong to one straight segment with a middle point. Verification mode computes the left side AB + BC and compares it directly with AC. If they do not match, the lengths do not satisfy the postulate for the stated point order. That makes the tool useful for catching diagram inconsistencies before they spread into later proof steps.
Matching sides confirm the postulate.
A nonzero difference means the data are inconsistent.
The difference output shows by how much the data miss the condition.
Verification is especially helpful when checking homework or worksheets quickly.
Common mistakes
The most common error is subtracting in the wrong direction, such as BC - AC instead of AC - BC. Another is forgetting that the whole segment must be at least as long as each part. Users also sometimes verify lengths that do not correspond to the stated point order and then wonder why the relation fails. Keeping the left side, right side, and difference visible helps make those errors obvious.
Do not subtract a whole from a part when solving for a missing length.
Do not assume the postulate applies without a middle point.
Do not forget that lengths should be positive.
Do not mix up which segment is the whole.
When people use this postulate
The segment addition postulate appears in introductory geometry, coordinate geometry, and proof writing. It is often the first bridge between a drawn picture and a variable equation. It also appears when checking distances on a number line, verifying collinearity setups, or splitting a segment into convenient subparts. Because the arithmetic is simple, the value of the calculator is mostly in avoiding setup and labeling mistakes.
Beginning geometry courses.
Proof and theorem exercises.
Distance checks on a line.
Worksheet verification and tutoring examples.
Manual method versus calculator method
You should still be able to do one-step segment-addition problems by hand, especially when the numbers are small. The calculator becomes useful when you want a fast correctness check, when you are handling many problems with similar structure, or when you want the explicit left-side versus right-side comparison shown on screen. A reliable habit is to say the relationship aloud—'part plus part equals whole'—before typing any numbers.
Speak the relationship before solving.
Use subtraction only when the whole and one part are known.
Check the difference output in verification problems.
Treat a negative would-be segment as a sign the setup is impossible.
Snabbreferenskort
Segment addition postulate quick reference
Snabbreferens • Kalkylator för segmentadditionspostulatet
AB + BC = ACGiltigt intervall: Use positive segment lengths with A, B, and C collinear and B between A and C.
Vanliga Värden
⚠ Se upp
- •The postulate depends on B being between A and C.
- •The whole segment must be at least as large as either part.
- •Negative or zero segment lengths do not fit the intended geometry context.
- •Verification can fail even when the arithmetic is simple if the point order is wrong.
Proffstips
- →Say 'part plus part equals whole' before rearranging the equation.
- →Use subtraction only when the whole and one part are already known.
- →Check the difference output to see how far inconsistent data miss the postulate.
- →Sketch the points in order if the labels feel confusing.
Vanliga Frågor
What does the segment addition postulate say?
It says that if B lies between A and C on a line, then AB + BC = AC.
When can I use AB + BC = AC?
You can use it when the points are collinear and B is between A and C.
How do I solve for a missing part?
Rearrange the equation. For example, AB = AC - BC and BC = AC - AB.
Why does verification mode matter?
It checks whether a set of three lengths is consistent with the postulate before you build more work on top of those values.
Can the whole segment be shorter than one of the parts?
No. If AC is the whole segment, it must be at least as large as AB and at least as large as BC.
What if the points are not in the order A-B-C?
Then this exact equation may not apply as written. The point order must match the statement that B lies between A and C.
Is this only for geometry class?
It is most common in geometry, but the same reasoning appears whenever a straight distance is split into adjacent pieces on a line or number line.