Thales's theorem (intercept theorem)

\dfrac{|AB|}{|BC|}=\dfrac{|A'B'|}{|B'C'|}

Result unit: — (proporcja)

What it describes

Parallel lines cutting the arms of an angle cut off proportional segments on them.

|AB|,|BC|

segments on one arm

|A'B'|,|B'C'|

segments on the other arm

Parallel lines cutting the arms of an angle divide them into proportional segments. This is the basis of similarity and scaling of figures.

Dividing segments, similarity of triangles, geometric constructions.

On one arm

|AB|=4

|BC|=6

; on the other

|A'B'|=2

. Find

|B'C'|

Substitution

\dfrac{4}{6}=\dfrac{2}{|B'C'|}

Result

|B'C'|=\dfrac{6\cdot2}{4}=3

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