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.