Move two matchsticks to create two identical triangles.
See picture below for couple of options
Here is a hexagon using 6 matchsticks. Move 4 matchsticks to create 2 triangles.
Move 4 matchsticks to create 5 triangles, the triangles don't have to be equal in size.
There are 3 rectangles of size 2X1 in the layout above. They are ABDC, EGLJ and FHMK.
Move 3 matchsticks to create FOUR equal rectangles each of size 2X1.
