Q:

How does Inkscape make a node segment smaller symmetrically?

In this YouTube video at this point in time the designer makes the node segment smaller symmetrically so that it stays centered by using the keyboard, but it does not show the shortcuts.
How is this done?

A:

You need to have the Show Transform Handles option selected in the tool controls along the top

Then use the Edit Paths by Nodes tool F2 to select the two nodes by clicking and dragging a selection around them
Hold down Shift as you click and drag the transform handles.

A:

I learn something new nearly every day:
From The Blog of the Baodad Tree website:

How To Make a Trapezoid in Inkscape

Draw a rectangle.
Convert it to a path (Path > Object to Path)
Use the node select tool (F2) to select the two corners of the
  rectangle that you want to adjust to form a trapezoid 
  (You have to hold down the shift key to select multiple nodes).
Press the comma or period keys to move apart or bring together the nodes.

