Question 53
(SWE 6) In making Euclidean constructions in geometry it is permitted to use a straightedge and compass. In the constructions considered in this question, no compasses are permitted, but the straightedge is assumed to have two parallel edges, which can be used for constructing two parallel lines through two given points whose distance is at least equal to the breadth of the ruler. Then the distance between the parallel lines is equal to the breadth of the straightedge. Carry through the following constructions with such a straightedge. Construct:
(a) The bisector of a given angle.
(b) The midpoint of a given rectilinear segment.
(c) The center of a circle through three given noncollinear points.
(d) A line through a given point parallel to a given line.
(a) The bisector of a given angle.
(b) The midpoint of a given rectilinear segment.
(c) The center of a circle through three given noncollinear points.
(d) A line through a given point parallel to a given line.