Explore the dynamic construction below.[br][list][*]Points A, B, and C are the endpoints of a triangle. These endpoints can be moved.[/*][*]The line through D and E is parallel to the line BC. Point D can be moved.[/*][/list]
What observations do you have about the construction? What questions come to your mind?
How do each of the labeled side lengths change as you adjust the position of D?
Can you find a proportional relationship in the construction? If so, what proportion can you find?[br][br]Note: a proportion is an equality statement between two ratios or fractions. Test different ratios to find two that are in proportion to one another.
https://www.geogebra.org/m/qjkez2ve