Turning on Smart Guides under the View menu will help.
A workaround would be to draw one polygon. Select it and note the height of the polygon.
Choose Object > Transform > Move. Enter the height measurement and click Copy.
Select both objects and rotate to the angle that you need.
Than you so much for your help! Can your method snap the corner vertices together? Because the two pologons are adjacent faces of an object, I need to snap them precisely and paint a scene across them. I know AutoCAD can do it, but wonder if illustrator can do the same thing.
I have found that usually it is easier to align objects when they are straight, rather than rotated. For example, if you wanted to snap the corners like this:
You could select both objects. Click on the object that you don't want to move (the key object). It will get a thicker line around it.
In the Align panel, if you click Horizontal Distribute Space with the spacing at zero, the objects will touch at the corners.