The elements fluorine, chlorine, and iodine are all part of the same blank space on the periodic table, which means they have the same

Fluorine, chlorine and iodine are all part of the same group on the periodic system. They are the halogens.

They contain the same number of valence electrons -- 7.

Explanation:

Those elements belong to the group seven elements and are also known as the halogens. Those are reactive non-metals and are always found blended with each other. The name halogen comes from Greek origin and ''hal'' means ''salt'' while ''gen'' means ''to produce'', because all of them produce sodium salts from similar properties. Those elements resemble one another because of their chemicals and in the properties of their compound with other elements. The most reactive of them is fluorine.

What they have in common --  they are all oxidizing agents. They raise the oxidation number of other elements which is a property that's used to be balanced with combination of oxygen and is now clarified in terms of  transfer of electrons from one atom to another.