Guess my Quad

Here is a game you could play with a friend...

Ask your friend to choose one of the shapes, and then try to identify which it is.
Your friend can only reply "Yes" or "No" to your questions. 

Then swap over.
Who can identify the other's shape with the fewest questions?
                             

Isosceles trapezium	Rectangle	Rhombus	Kite
Parallelogram	Square	Trapezium	Arrowhead

 

You may wish to print out this sheet to record the answers and help you eliminate possible shapes.

Here are some questions you might like to consider:

How many questions do you need to ask to guarantee you know your friend's shape?
What would you ask first?
If your friend says "Yes", what would you ask next? 
If your friend says "No", what would you ask next?

Charlie says he can always identify Alison's shape after asking just three questions.
Which question might Charlie ask first? Which follow-up questions might he then ask? 

Can you invent a game with more shapes, where you can always identify your friend's shape in four questions? What is the maximum number of shapes you could have in such a game?

With thanks to Don Steward, whose ideas formed the basis of this problem.