Intercept theorem

Intercept theorem Teorema di Talete Thorme de Thals مبرهنة طاليس अवरोध प्रमेय 截线定理 Stelling van Thales Teorema de Tales Teorema da interceptao

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 Sketch for the intercept theorems
Segment ZA : Segment ZA' :

Segment ZB : Segment ZB' :

Segment AB : Segment A'B' :

This is the typical situation for the intercept theorem: Two parallel lines are intersecting two other intersecting lines. Now you can compare distances between intersection points and can see that these formulas hold:

Strahlensatz - Figur

First intercept theorem: ZA'/ZA=ZB'/ZB Second intercept theorem: A'B'/AB=ZA'/ZA
or A'B' / AB = ZB' / ZB
This means the first intercept theorem tells something about the relation of parts of the intersecting lines while the second intercept theorem also includes distances on the parallel lines.