Proportionality Theorems

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Task 1:
Move point E such that [math]\overline{DE}[/math] divdes [math]\overline{AB}[/math] and [math]\overline{BC}[/math] proportionally.
Question on Task 1:
Upon completing the task 1, make a conjecture about how [math]\overline{DE}[/math] relates to the other sides in the triangle. Confirm your conjecture using the meausurement tools in the sketch window, and explain your conjectrue below.
Task 2;
In the sketch below, move point D such that [math]\overline{CD}[/math] bisects [math]\angle[/math]C.
Question on Task 2:
Upon completing task two, make a conjecture about the lengths of the segments formed when an angle bisector intersects the opposite side of a triangle.
Task 3:
Create lines [math]\overline{GH}[/math] and [math]\overline{IJ}[/math] such that [math]\overline{EF}\parallel\overline{GH}\parallel\overline{IJ}[/math] (let [math]\overline{CD}[/math] contain points H and J)
Question on Task 3:
Using the measurement tools, identify a proportion. Write a theorem which describes what happens when three parallel lines intersect two transversals. (Hint: your laptop's calculator app can help verify your proportion).
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Information: Proportionality Theorems