Guided Discovery: There are sliders for AB and DC. Explore these sliders and see what relationships you think may hold. Exploring angle and segment relationships: 1. Set AB = 4 and DC = 10. 2. What quadrilateral is created? 3. How many of those quadrilaterals can you find? 4. List as many relationships between the angles in these quadrilaterals as you can find. 5. Make a conjecture as to how AB, EF, and DC are related. Why? 6. What relationships do you see between the segment lengths? 7. What conjecture can you make about the location of points E and F? 8. Write an equation to calculate EF? 9. As you move the sliders, does your equation always work? 10. Will this equation work for all triangles? If not provide counterexamples. 11. Will this equation work for all quadrilaterals? If not provide counterexamples. 12. What conditions must be met for this equation to work every time?