Why are the halogens less reactive going down the periodic table ?

The main reason why the halogens decrease in reactivity down the group is because of the increasing atomic radius going down the group from Fluorine to Astatine.  As you move down the group, there is an increase in the electronic shell which leads to an increase in the distance from the nucleus to the valence shell (atomic radius).  Because of this increase, the valence electron is increasingly further from the nucleus as you move down the group,which result in the pull on that valence electron being weaker; hence the weakening in the reactive power.

If you imagined the line BCD as a line and ACE as a transversal, this would make angle ACB and DCE alternate interior angles. Since all three angles in a triangle, add up to 180 degrees, this means that the side lengths should be similar or congruent to accommodate the angle measure.