DE intersects Triangle ABC and is parallel to side AC. Drag any point on ABC to adjust the triangle. Drag D to adjust DE up or down the sides of the triangle. The text on the left provides the measure of the segments and their ratios.
1. Move D to change segment DE's position. What do you notice about the ratios BD/DA and BE/EC?
2. Adjust points A, B, and C to change the triangle. Again, move D to change segment DE's position. Does the rule about the ratios from #1 still hold?
3. Can you make the ratios equal 1? What can you say about segment DE when the ratio of BD/DA = 1?
4. What can you say about the relationship of triangle ABC to triangle DBE? Justify your answer. Will this always be true?