Side Splitter Exploration
1) Click the first checkbox to create a parallel line through D. What line is this parallel to?
2) Click the next box that says "Show distances." Look at the distances AD, CD, BE, CE. Drag D around to make the distances longer and shorter. If you notice any relationships, type them here. If not, move on to the next question.
3) Click the third box that says "Show ratios." Drag all the points and see what happens. They are dividing AD by CD and dividing BE by CE. No matter what the side lengths are, the ratios are always the same. Why do you think that's happening? If you're not sure, that's OK, but think of a question to ask! :)
4) They identified ONE of the proportional relationships that exists on this figure: What other proportional relationships do you think might exist?