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Thales' Theorem

Parallel lines cut proportional segments — statement, examples, and a proportions trainer.

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Thales' Theorem — the essentials

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Frequently Asked Questions

What does Thales' theorem state?

Parallel lines intersecting two lines cut off proportional segments: AB/BC = DE/EF.

How do you apply Thales' theorem?

If AB=4, BC=6, DE=6, find EF: 4/6=6/EF → EF=9.

What is a corollary of Thales' theorem?

The midsegment of a triangle is parallel to the base and equals half the base.