Here's the deal with Construction Geometry. First, it may help if you think of Construction geometry as being like the pencil lines you might draw on a piece of wood for layout. Of course with Construction Geometry the lines can locate points in space or extend off the edge of a "board" and into space.
You can create reference points or lines to draw off of or to use for locating components or other geometry. Use Construction Geometry to lay out a joint and then trace along with the Pencil tool to make the cuts.
There are Construction Lines and Construction Points. I'm going to call them X-lines and X-points. X-points are drawn with the Tape Measure tool. X-lines are drawn with either the Tape Measure or Protractor tool.
X-lines drawn with the Tape Measure tool are drawn parallel to some other line. You have to reference off another line--not a point or intersection. The line can be an axis, a line or edge in some geometry, or another X-line.
To draw an X-line with the Tape Measure tool, select the tool. Hold Ctrl while clicking on a line and then drag off in the desired direction. Watch for the direction indicators--the trailing line that matches the color of the axis. Also watch for the little pop up messages that sometimes appear. After you start dragging out the X-line you can click again and then let go of everything and then type a distance. Hit Enter. You could also drag the line to some other reference if that works.
To draw an X-point with the Tape Measure tool, start from an intersection. You'll end up with a tiny little x marking the point. Remember to hold the Ctrl key.
Now, to set an X-line at an angle, use the Protractor tool. Select the tool, hold Ctrl and click on the point at which you wish the X-line to intersect. Drag out from that point along the line of in whatever direction your angle is based off. Click. Now start dragging in the desired direction. Click again. Type the desired angle if need be and hit Enter.
Hopefully that helps you get some Construction Geometry drawn. As a side note, open a new session of SU. Don't draw anything. Go to Window>Preferences>Shortcuts. Scroll through the list to find Edit/Construction Geometry/Erase All and set a shortcut that is easy to remember. I use E. Click in and type the shortcut in the Add shorcut box. Click on the + button to the right of it. Close the Preferences dialog and do a Save as and save the blank drawing in the Template folder under Google SketchUp. That should save the shortcut.