perpendicular bisector of a line segment

perpendicular to a line at a point on a line

perpendicular to a line from an external point

Draw an arc across the line on each side of R, making sure not to adjust the compasses' width in between. Label these points P and Q

Place the compasses on the given external point R.

Place a straightedge between R and the point where the arcs intersect. Draw the perpendicular line from R to the line, or beyond if you wish.

A parallel to a line through a point (angle copy method)

A parallel to a line through a point (rhombus method)

A parallel to a line through a point (translated triangle method)

Copy an angle

Set the compasses' width to the distance where the lower arc crosses the two lines

Move the compasses to where the upper arc crosses the transverse line and draw an arc across the upper arc, forming point S

There are no more steps

Draw an arc across both sides of the angle, creating the points J and K.

Step 4

Draw a ray PR from P through L and onwards a little further.

Make a point P that will be the vertex of the new angle.

a square

a square given one side

a square inscribed in a circle

a rectangle

Without changing the width, move the compasses to C. Draw an arc to the left of C across the exiting arc, creating point D - a vertex of the square.

There are no more steps

Draw the lines CD and AD

Draw a perpendicular line to AB

Draw a diameter line from the point A, through the center and on to cross the circle again, creating point C.

Mark a point A on the circle

Draw an arc above and below O.