Question: Why is there a stair-shaped line between metals and nonmetals on the periodic table?
About the article "Periodic table", section "Metallic character".

Candidate passages:
The dividing line between metals and nonmetals can be found, in varying configurations, on some representations of the periodic table of the elements (see mini-example, right).
Elements to the lower left of the line generally display increasing metallic behaviour; elements to the upper right display increasing nonmetallic behaviour.
When presented as a regular stair-step, elements with the highest critical temperature for their groups (Li, Be, Al, Ge, Sb, Po) lie just below the line. 
A dividing line between metals and nonmetals is sometimes replaced by two dividing lines.
One line separates metals and metalloids; the other metalloids and nonmetals. 
The lower the values of ionization energy, electronegativity and electron affinity, the more metallic character the element has.
Conversely, nonmetallic character increases with higher values of these properties.
Given the periodic trends of these three properties, metallic character tends to decrease going across a period (or row) and, with some irregularities (mostly) due to poor screening of the nucleus by d and f electrons, and relativistic effects, tends to increase going down a group (or column or family).
Thus, the most metallic elements (such as caesium and francium) are found at the bottom left of traditional periodic tables and the most nonmetallic elements (oxygen, fluorine, chlorine) at the top right.
The combination of horizontal and vertical trends in metallic character explains the stair-shaped dividing line between metals and nonmetals found on some periodic tables, and the practice of sometimes categorizing several elements adjacent to that line, or elements adjacent to those elements, as metalloids.
Several terms are commonly used to characterize the general physical and chemical properties of the chemical elements.
A first distinction is between metals, which readily conduct electricity, nonmetals, which do not, and a small group, (the "metalloids"), having intermediate properties and often behaving as semiconductors.
A more refined classification is often shown in colored presentations of the periodic table.
This system restricts the terms "metal" and "nonmetal" to only certain of the more broadly defined metals and nonmetals, adding additional terms for certain sets of the more broadly viewed metals and nonmetals.
The version of this classification used in the periodic tables presented here includes: actinides, alkali metals, alkaline earth metals, halogens, lanthanides, other metals; metalloids, noble gases, polyatomic nonmetals, diatomic nonmetals, and transition metals.
In this system, the alkali metals, alkaline earth metals, and transition metals, as well as the lanthanides and the actinides, are special groups of the metals viewed in a broader sense.
Similarly, the polyatomic nonmetals, diatomic nonmetals and the noble gases are nonmetals viewed in the broader sense.
In some presentations, the halogens are not distinguished, with astatine identified as a metalloid and the others identified as nonmetals. 
Elements by periodic table can be divided up into metal, nonmetal, and metalloids (in between) based on their properties.
Everything from the left to the metalloid "stairstep" is a metal, and everything to the right is a nonmetal.
The periodic table shows most elements are metals.