Question 130
Line *r* passes through the corner $A$ of a sheet of paper and makes an angle $\alpha$ with the horizontal border, as shown in figure 1. In order to divide $\alpha$ into three equal parts we proceed as follows:
a) initially we mark two points $B$ and $C$ on the vertical border such that $AB = BC$; through $B$ we draw a line $s$ parallel to the border (figure 2);
b) after that, we fold the sheet so as to make $C$ coincide with a point $C'$ on the line $r$ and $A$ with a point $A'$ on line $s$ (figure 3); we call $B'$ the point which coincides with $B$.
Figure 1
Figure 2
Figure 3
Show that lines $AA'$ and $AB'$ divides angle $\alpha$ into three equal parts.
a) initially we mark two points $B$ and $C$ on the vertical border such that $AB = BC$; through $B$ we draw a line $s$ parallel to the border (figure 2);
b) after that, we fold the sheet so as to make $C$ coincide with a point $C'$ on the line $r$ and $A$ with a point $A'$ on line $s$ (figure 3); we call $B'$ the point which coincides with $B$.
Figure 1
Figure 2
Figure 3
Show that lines $AA'$ and $AB'$ divides angle $\alpha$ into three equal parts.