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Mathematics
Triangle proportionality — Parallel lines preserve ratios
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Triangle ABC has M on AB and N on AC. Drag MN while it stays parallel to BC, or release the constraint and move either intersection. Compare the measurements and ratios in the observation panel.
MN ∥ BC
Model measurements (cm)
Drag MN; compare AM/AB and AN/AC.
Select or focus a segment name in a fraction to highlight it in the diagram.
The two ratios are equal
MN is parallel to BC
=
5.213
=0.400=
615
=0.400Displayed measurements are rounded; comparisons use the model values.
- AM
- 5.2 cm
- MB
- 7.8 cm
- AN
- 6 cm
- NC
- 9 cm
- AB
- 13 cm
- AC
- 15 cm
If MN ∥ BC, with M on AB and N on AC, corresponding segments on the two sides have equal ratios.
As MN moves, the common value can change. What stays true is that the two ratios are equal.
Model notes
- The model uses nondegenerate triangles, with M inside AB and N inside AC. The 10–90% control range keeps the diagram readable; the theorem is not limited to that range.
- Lengths are centimetres in an ideal model. Displayed numbers are rounded, but comparisons use original values; screen sizes are not physical ruler measurements.
- Releasing the constraint lets the points move independently; the lines can still be parallel when both points divide their sides at the same fraction.
- The interaction illustrates the theorem and does not replace a general proof. This version does not cover intersections on extended sides or directed lengths.