Segment Addition Postulate
If B is between A and C, then AB + BC = AC. Find total (AC), find part (BC), or verify the postulate.
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AB + BC = AC — The Segment Addition Postulate
Find total, find part, or verify. If B is between A and C, then AB + BC = AC.
📐 Examples — Click to Load
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For educational and informational purposes only. Verify with a qualified professional.
📋 Key Takeaways
- • The Segment Addition Postulate: If B is between A and C, then AB + BC = AC
- • Use find-total when you know AB and BC and need AC (e.g., ruler segments)
- • Use find-part when you know AC and AB and need BC (e.g., beam sections)
- • Use check-collinear to verify that three given lengths satisfy the postulate
- • The postulate applies only when points A, B, C are collinear with B between A and C
💡 Did You Know?
📖 Formulas
Find Total
Find Part
Find Part
🎯 Expert Tips
💡 Ruler Analogy
Think of a ruler: the distance from 0 to 5 plus 5 to 10 equals 0 to 10. AB + BC = AC.
💡 Order Matters
B must be between A and C. If A is between B and C, then BA + AC = BC, not AB + BC = AC.
💡 Algebra Setup
For AB=2x+1, BC=3x, AC=21: (2x+1)+3x=21 → 5x+1=21 → x=4. Then AB=9, BC=12, AC=21 ✓
💡 Verification
When checking, AB + BC should equal AC within rounding. Small differences indicate measurement error.
📊 Quick Facts
❓ FAQ
What is the Segment Addition Postulate?
If point B is on segment AC (between A and C), then AB + BC = AC. It's a fundamental axiom in Euclidean geometry.
When does the postulate apply?
Only when A, B, and C are collinear and B is between A and C. If they form a triangle, AB + BC > AC.
How do I find AC given AB and BC?
Use find-total mode: AC = AB + BC. Example: AB=3, BC=5 → AC=8.
How do I find BC given AC and AB?
Use find-part mode: BC = AC − AB. Example: AC=10, AB=4 → BC=6.
What if AB + BC ≠ AC?
Then either the points aren't collinear, B isn't between A and C, or there's measurement error.
Can I use this with algebraic expressions?
Yes. If AB=2x+1, BC=3x, AC=21, then (2x+1)+3x=21 → 5x=20 → x=4. Verify: 9+12=21 ✓
Does it work in 3D?
Yes. The postulate holds for collinear points in any dimension. Use the 3D distance formula.
Why is it called a postulate?
A postulate is an assumption accepted without proof. Euclid used it as a building block for geometry.
📚 Sources
⚠️ Disclaimer: This calculator assumes collinear points with B between A and C. For non-collinear or different order, the postulate does not apply.
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