Plastic is a common material used in crafts and household repairs. To join two plastic sheets, the sheets can either be glued (preferably with a good epoxy) or fused together. If the actual composition of the plastic is unknown, an epoxy is the best choice as it will survive longer than the plastic sheets themselves.
Clean the two pieces of plastic to be epoxied together. The epoxy will fail if the pieces are not clean. Paint, stickers and the like should also be removed at the bonding site.
Mix the two parts of the epoxy together on a piece of aluminium foil using a wooden stick. This is typically done in a 1:1 mixture for one to two minutes.
Coat the bonding edge of one of the pieces of plastic. The coating should be thin enough to cover the entire surface but not squeeze out when the two pieces are combined.
Place the second piece of plastic onto the epoxy coating. Gently squeeze the two pieces together for five minutes.
Allow to sit for 24 hours. The epoxy will harden and should be stronger than the actual plastic.
DO NOT allow the epoxy to come in contact with anything you do not intend on gluing. Epoxies are extremely difficult to remove once they have made contact. Once an epoxy sets up, they are nearly impossible to break without destroying the material it is bonded to. Epoxies also cause heat when bonding, some hot enough to cause contact burns.