Isomers are compounds with the same chemical formula but different structures. An important test of Werner's theory of coordination complexes involved the study of coordination complexes that formed isomers (literally, "equal parts").
Example: There are two isomers for the Co(NH3)4Cl2+ complex ion, as shown in the figure below.
The structures of these isomers differ in the orientation of the two chloride ions around the Co3+ ion. In the trans isomer, the chlorides occupy positions across from one another in the octahedron. In the cis isomer, they occupy adjacent positions. The difference between cis and trans isomers can be remembered by noting that the prefix trans is used to describe things that are on opposite sides, as in transatlantic or transcontinental.
At the time Werner proposed his theory, only one isomer of the
[Co(NH3)4Cl2]Cl complex was
known 
the green complex. Werner predicted that a second isomer should
exist and his discovery in 1907 of a purple compound with the
same chemical formula was a key step in convincing scientists who
were still critical of his model.
Cis/trans isomers are also possible in four-coordinate complexes that have a square-planar geometry. The figure below shows the structures of the cis and trans isomers of dichlorodiammineplatinum(II). The cis isomer is used as a drug to treat brain tumors, under the trade name cisplatin. This square-planar complex inserts itself into the grooves in the double helix structure of the DNA in cells, which inhibits the replication of DNA. This slows down the rate at which the tumor grows, which allows the body's natural defense mechanisms to act on the tumor.
Another form of isomerism can be understood by considering the difference between gloves and mittens. One glove in each pair fits the left hand, and the other fits the right hand. Mittens usually fit equally well on either hand. To understand why, hold a glove and a mitten in front of a mirror. There is no difference between the mitten shown in the figure below and its mirror image. There is a difference, however, between the glove and its mirror image. The mirror image of the glove that fits the left hand looks like the glove that fits the right hand, and vice versa.
Each member of a pair of gloves is the mirror image of the other the way the right and left hands are mirror images of each other. Gloves therefore have the same property as the hands on which they are placed. As a result, they are said to be chiral (from the Greek cheir, hand). By definition, any object that has a mirror image that is different from itself is chiral. The Co(en)33+ ion is an example of a chiral molecule, which forms a pair of isomers that are mirror images of each other (see figure below). These isomers have almost identical physical and chemical properties. They have the same melting point, boiling point, density, and color, for example. They differ only in the way they interact with plane-polarized light.
Polarized Light and Optically Active Compounds
Light consists of electric and magnetic fields that oscillate in all directions perpendicular to the path of the light ray. When light is passed through a polarizer, such as a lens in a pair of polarized sunglasses, these oscillations are confined to a single plane. Compounds that can rotate plane-polarized light are said to be optically active. Those that rotate the plane of polarization to the right (clockwise) are said to be dextrorotatory (from the Latin dexter, "right"). Those that rotate the plane to the left (counterclockwise) are levorotatory (from the Latin laevus, "left"). All chiral compounds are optically active; one isomer is dextrorotatory and the other is levorotatory.