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Triangle Proportionality Theorem Calculator — result sheet
Solve a missing side segment when a line parallel to a triangle base creates two proportional smaller sides.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: If the inner segment is parallel to the triangle base, upper-left/full-left = upper-right/full-right. With full-left = upper-left + lower-left, the missing lower-right segment is upper-right × lower-left ÷ upper-left.
A line parallel to one side of a triangle creates a smaller triangle similar to the original. This calculator uses that relationship to solve the missing segment and then reports both complete side lengths and the matching ratios as a visible check.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Upper left segment — length units; minimum 1.0E-6; maximum 1000000000
- Lower left segment — length units; minimum 1.0E-6; maximum 1000000000
- Upper right segment — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Upper left segment | 4 |
| Lower left segment | 6 |
| Upper right segment | 5 |
Lower-right segment =7.5; full left side =10; full right side =12.5; scale factor =2.5.
Assumptions and limits
- The inner segment is genuinely parallel to the triangle's base.
- All three entered segments are positive and use one consistent length unit.
- The upper and lower segments lie on corresponding sides of one non-degenerate triangle.
- The relationship is Euclidean and planar.
- The tool does not determine angles, coordinates, or whether a drawn line is actually parallel.
- The result is an ideal proportion calculation, not a tolerance or surveying adjustment.
- Rounding is applied only to displayed outputs.
- If the line is not parallel, use a different triangle model.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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