(1) Construct a perpendicular to through $B$

Step 1 ：Draw a line segment AB.

Step 2 ：Place the compass at point B, draw an arc cutting the line segment at some point (let's call it C).

Step 3 ：Without changing the compass width, draw another arc below the line segment AB.

Step 4 ：Keeping the compass at point C, draw another arc cutting the previous arc. Let's call this intersection point D.

Step 5 ：Draw a line from B through D. This line is the perpendicular to AB through B.