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Side-Splitting

The Side-Splitting Theorem states that a line parallel to one side of a triangle divides the other two sides proportionally.

BC is parallel to DE.
You can change the shape of the triangle by clicking a vertex, and dragging it around.
You can move the middle segment by clicking point B, and moving it up and down.

Here, we can watch the lengths of the upper right, lower right, total right, upper left, lower left, and total left change as you move around the triangle!

One proportion suggested by the Side-Splitting Theorem is:

Upper Right/ Lower Right = Upper Left/ Lower Left

We can see that this always holds true by the given calculations.

Can you observe any other proportions?

Try Upper Right/ Total Right = Upper Left/ Total Left

Does this work as well?

Can you think of any other proportions that may work?

Move the triangle around and see if the proportions always work so long as BC is parallel to DE.