(1)
Construct a perpendicular to through $B$
Draw a line from B through D. This line is the perpendicular to AB 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.