Step 1 (Characteristics of transition metals):
1. They show variable oxidation states (for example Fe as +2 and +3, Mn from +2 to +7).
2. Their ions and compounds are usually coloured because of d-d electronic transitions.
3. Many are paramagnetic due to the presence of unpaired d-electrons.
4. They and their compounds often act as good catalysts (for example Fe in the Haber process, V\(_2\)O\(_5\) in the contact process).
5. They readily form complex (coordination) compounds because of small size and high charge.
6. They form alloys and interstitial compounds, and have high melting and boiling points, high density and good hardness (strong metallic bonding using d-electrons).
Step 2 (Why they are called transition metals): They are placed in the middle of the periodic table between the strongly electropositive s-block metals on the left and the p-block elements on the right. They represent a gradual transition (change) in properties from the highly reactive s-block to the less metallic p-block.
Step 3: They are formally defined as elements whose atoms or stable ions have partly filled d-orbitals, which is the source of all the above properties.