Stage 17 · Similarity & Dilation

17.2.2 The Parallel-Line Proportionality Theorem

17.2 Parallel Lines Cut Segments Proportionally

Point 2 of 4

17.2.2 The Parallel-Line Proportionality Theorem

Core idea

A bundle of parallel lines acts like a bread slicer, and the matching pieces it cuts from two crossing lines all share the same length ratio.

Module goal. Using the parallel lines you already know well as a tool, we discover that 'parallel lines slice by the same ratio,' which is the direct source of the tests for similar triangles.
eastmath.com · 17.2 Parallel Lines Cut Segments Proportionally · 17.2.2 The Parallel-Line Proportionality Theorem