Proportionality Theorems (similarity)

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.