1. Define Segments
Leave one field blank to solve for it.
2. Solution
How to Use the Calculator
Solve segment addition problems in three simple steps. Our tool handles numbers and algebraic expressions with ease.
Input Known Values
Enter the lengths for the two segments you know. You can use numbers (e.g., 7) or expressions with 'x' (e.g., x+5).
Leave One Blank
Leave the field for the unknown segment length empty. The calculator will automatically identify what needs to be solved.
Calculate & Analyze
Click "Calculate" to see a complete solution, including the value of x, the final segment lengths, and an updated diagram.
An Interactive Learning Tool
This calculator goes beyond simple answers by providing a detailed breakdown and visual feedback to help you master the concept.
- Algebraic Solver: Intelligently solves for 'x' when given expressions, setting up and solving the underlying equation for you.
- Dynamic Visualization: The line segment diagram updates in real-time to visually represent the proportions of the solved lengths.
- Smart Error Handling: The calculator detects invalid inputs, impossible geometric scenarios, and solutions that would result in negative lengths.
Understanding the Postulate
The Segment Addition Postulate is a fundamental rule in Euclidean geometry. Here's a breakdown of the concept and how to apply it.
What is the Segment Addition Postulate?
The postulate states that if you have three points—A, B, and C—that are collinear (all on the same line), and point B is located between points A and C, then the length of the segment AB plus the length of the segment BC is equal to the total length of the segment AC.
What is the formula?
The formula is a straightforward representation of the postulate:
AB + BC = AC
This simple equation is the basis for solving all problems related to the postulate. Our calculator uses this formula to solve for the unknown value you provide.
How do you solve problems involving algebra?
To solve an algebraic problem, you substitute the given expressions into the formula. For example, if AB = x + 2, BC = 3x, and AC = 14:
- Set up the equation:
(x + 2) + (3x) = 14 - Combine like terms:
4x + 2 = 14 - Isolate the variable:
4x = 12 - Solve for x:
x = 3
You can then plug x=3 back into the original expressions to find the lengths: AB = 5 and BC = 9.
