Triangle Proportionality Theorem Calculator
If a line DE is drawn parallel to side BC of triangle ABC, it divides the other two sides proportionally: AD/DB = AE/EC. Enter any three of the four segments to find the fourth.
Found from AD/DB = AE/EC → EC = AE × DB / AD
- 1
Proportion ratio AD ÷ DB
4 ÷ 6 = 0.6667By the Triangle Proportionality Theorem, AD/DB = AE/EC. - 2
EC = AE × DB ÷ AD
5 × 6 ÷ 4 = 7.5000
How does this calculator work?
If line DE ∥ BC in triangle ABC (D on AB, E on AC), then AD/DB = AE/EC. To find EC: EC = AE × DB / AD. Enter AD, DB, and AE — the calculator returns EC, both full side lengths, and the splitting ratio in one step.
Formula
How this is calculated
The Triangle Proportionality Theorem (also called the Basic Proportionality Theorem or Side-Splitter Theorem) states that if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio. In triangle ABC, if line DE is parallel to BC with D on AB and E on AC, then AD/DB = AE/EC. Rearranging, the missing segment EC = AE × DB / AD.
The theorem follows from the AA (Angle-Angle) similarity criterion: triangle ADE is similar to triangle ABC because corresponding angles are equal (the parallel line creates equal alternate interior angles). Similar triangles have proportional sides, which gives the ratio above.
The ratio AD/DB also equals the "position" of the parallel line along the triangle: AD/AB = AE/AC = DE/BC, so the parallel line cuts all measurements from vertex A in the same proportion. This makes the theorem useful in scale drawings, map reading, and engineering cross-sections.
Frequently asked questions
The converse states that if a line divides two sides of a triangle in equal ratios (AD/DB = AE/EC), then the line is parallel to the third side. You can use this to verify parallelism from measurements alone.
No — DE must be a transversal cutting both sides AB and AC between the vertices, not at them. If D coincides with A or B (or E with A or C), the segments collapse to zero or the full side, and the ratio is undefined or trivial.
Yes — the theorem holds for any triangle (scalene, isosceles, equilateral, acute, obtuse or right) as long as DE is parallel to BC. The shape of the triangle does not affect the proportionality.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Proportionality Theorem Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-proportionality-theorem-calculator
TG we-Calculate Editorial Team. "Triangle Proportionality Theorem Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-proportionality-theorem-calculator.
TG we-Calculate Editorial Team, "Triangle Proportionality Theorem Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-proportionality-theorem-calculator
@misc{wecalculate_triangle_proportionality_theorem_calculator, title = {Triangle Proportionality Theorem Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-proportionality-theorem-calculator}}, year = {2026}, note = {TG we-Calculate} }
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