What properties of light allow shadows to form?
Reflection and also the fact that light propagates in a rectilinear way (straight lines).
Whenever light(and waves in general) reach an obstacle, they bounce off.
Shadows appear simply because, the light that was falling on that area or spot is being shielded.
We see shadows because, there is more light in the surroundings that than there is light at the shadow area.
That's why you cannot see a shadow in a dark room.
The way shadows are formed in such a way that the shape of the shadows resembles the object is because light travels in straight lines.
This means that, a light ray wouldn't just jump up the obstacle and land on the other side and then you would see some funny light spots on the shadow.
Hope I've hit the point home.