Given the lengths of the sides of a triangle, construct it.

Here the lengths are AB=10, BC=8 and AC=6 (to start with).
D and E lie between A and B so that AE=AC and BD=BC.
You can move the points A, B, D and E.
Note what happens to C as you move D towards B ...
What about when D reaches E ... and moves to beyond E (towards B)?
Move D back again between A and E, noticing all the while ...
Next, leave D fixed and move E ...
Finally move A (or B) so that AB is no longer horizontal ...
Write down everything your notice ...