``

and shares a common side . Line intersects line at . This theorem says that
.
There're 4 possible cases depending on how the 2 pairs of points and are divided by the 2 lines and .
\ | same side | diff side |

same side | (a) | (b) |

diff side | (c) | (d) |

The usual proof involves simple arithmetic manipulations on fractions.
This activity aims at providing a constructive proof without words that works for *all* cases. The principle is to transform into a triangle with equal area and a base , then a similar construction for .## Click either one of the unchecked and move point A' and observe the transformed triangles.