Triangle Proportionality Theorem Calculator

Check if a line parallel to one side of a triangle divides the other two sides proportionally (Side Splitter Theorem).

Enter Segment Lengths

Line DE is parallel to side BC. D is on AB, E is on AC. Enter the four segment lengths.

Result

Proportionality Check
--
Ratio AD/DB --
Ratio AE/EC --
Difference --

Step-by-Step Solution

AD / DB = AE / EC

Triangle Proportionality Theorem (Side Splitter Theorem)

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. This is also known as the Side Splitter Theorem or the Basic Proportionality Theorem (Thales' theorem in some traditions).

The Theorem Explained

Direct Proportion

If DE is parallel to BC in triangle ABC, then:

AD / DB = AE / EC

Converse

If a line divides two sides proportionally, it is parallel to the third side.

AD/DB = AE/EC implies DE || BC

Extended Form

The theorem can also be written using the full side lengths.

AD/AB = AE/AC = DE/BC

How to Use This Calculator

In Check Proportionality mode, enter all four segment lengths (AD, DB, AE, EC) to verify whether the ratios are equal. In Find Missing Segment mode, enter three known values and leave the fourth blank to solve for the unknown segment using the proportionality relation.

Practical Applications

  • Architecture: Dividing beams or structural elements proportionally.
  • Mapping: Creating scaled sections of triangular regions.
  • Computer Graphics: Texture mapping and interpolation along triangle edges.
  • Engineering: Proportional load distribution in triangular trusses.