Segment Addition Postulate Calculator — Find a Missing Segment or Check Collinearity

The segment addition postulate calculator allows you to apply this property by adding the lengths of two adjacent segments and finding the value of the total segment. Below, we'll also cover the definition of the segment addition postulate, how the segment addition calculator works, and worked examples of the segment addition postulate.

What is the segment addition postulate?

The definition of the segment addition postulate states that if we have a line segment AC and a point B within it, the sum of the lengths of the segments AB and BC will give the total length of AC.

AC = AB + BC

In other words, three points A, B, and C are collinear (they lie on the same straight line, with B between A and C) exactly when the two shorter pieces add up to the whole.

How do we use the segment addition postulate?

Given a line segment AC and a point B in between, if we know the lengths AB and BC, we can find AC using the equation AC = AB + BC.

The segment addition property (which is based on the distances between points) is used in this segment addition postulate calculator, which also helps you find out if a particular point lies on a line segment when the lengths are known. If the sum of the segments equals the total length, the points must be on the same line, and we say they are collinear. The calculator can check whether this is the case when you select the mode "Check if points are collinear".

Segment addition postulate example

For instance, in a line segment AC, if you know that AB = 10 cm and BC = 20 cm, here's how you can find the total length of AC:

1. Enter 10 cm for AB in the segment addition postulate calculator;
2. Enter 20 cm for BC; and
3. Voilà! Using the segment addition property, we can see that the total length of AC is 30 cm!

AC = AB + BC = 10 + 20 = 30 cm

The extra-cool feature is that if you know the total length and the length of one segment, the calculator will automatically find the length of the other segment for you. Just leave the unknown field blank — for example, enter AC = 30 cm and AB = 10 cm, and the calculator returns BC = 20 cm.

Segment bisector

A segment bisector is a point, line, ray, or segment that divides a line segment into two equal halves. If B is the midpoint (bisector point) of AC, then AB = BC, and each half is exactly one-half of the total:

AB = BC = AC / 2

You can confirm a bisector with this calculator: if the two segments you enter are equal and their sum matches the total AC, then B bisects the segment.

How do we use the segment addition postulate practically?

The segment addition postulate is more than a textbook rule — it shows up whenever a whole is split into adjacent parts along a straight path:

• Construction and carpentry: adding board or beam lengths that meet end-to-end to get a total run.
• Maps and travel: a trip from A to C that stops at B has a total distance equal to AB + BC when the route is straight.
• Geometry proofs: solving for an unknown length or setting up algebraic equations such as AB + BC = AC when the pieces are given as expressions in x.
• Coordinate geometry: verifying that a point lies on a segment by checking collinearity.

Metric vs. US (Imperial) Units

This calculator supports both measurement systems, and the segment addition postulate is unit-agnostic — the mathematics is identical regardless of units:

• Metric system: millimeters (mm), centimeters (cm), meters (m), kilometers (km).
• US / Imperial system: inches (in), feet (ft), yards (yd), miles (mi).

Just enter every length in the same unit, and the result is expressed in that same unit.

How to use the segment addition postulate calculator

1. Choose what you want to do: find a missing length or check if points are collinear.
2. Pick your unit system (metric or US) and the unit of measurement.
3. To find a missing length, fill in any two of AB, BC, and AC, and leave the third blank — the calculator finds it.
4. To check collinearity, enter all three lengths (AB, BC, AC); the calculator confirms whether AB + BC = AC.
5. Read the result, a segment diagram, and a full step-by-step solution.

FAQs

What does the segment addition postulate state?

If point B lies on segment AC (between A and C), then AB + BC = AC. The two adjacent parts add up to the whole segment.

How do I find a missing segment length?

Enter the two lengths you know and leave the third blank. If you know AC and AB, the calculator computes BC = AC − AB; if you know AC and BC, it computes AB = AC − BC; and if you know AB and BC, it computes AC = AB + BC.

How can the postulate check collinearity?

If A, B, and C are collinear with B between A and C, then AB + BC must equal AC. If AB + BC is greater than AC, the point B cannot lie on the straight segment AC, so the points are not collinear in that arrangement.

What is a segment bisector?

A segment bisector splits a segment into two equal halves. If B bisects AC, then AB = BC = AC / 2.

Can a segment length be negative?

No. Lengths are always zero or positive. If solving for a missing piece gives a negative value, the given total is too small — double-check your inputs.