how do you construct congruent segments, segment bisectors, angles, angle bisectors using tools such as compass and straightedge?

Question

anonymous · Answer

To bisect a segment or an angle means to divide it into two congruent parts. A bisector of a line segment will pass through the midpoint of the line segment. A perpendicular bisector of a segment passes through the midpoint of the line segment and is perpendicular to the line segment. In order to construct bisectors of segments and angles, it's helpful to remember some relevant theorems:
Any point on the perpendicular bisector of a line segment will be equidistant from the endpoints of the line segment. This means that one way to find the perpendicular bisector of a segment (such as   \overline{AB} below) is to find two points that are equidistant from the endpoints of the line segment (such as   C and  D below) and connect them.  
 
Any point on the angle bisector of an angle will be equidistant from the rays that create the angle. This means that one way to find the angle bisector of an angle (such as  \angle BAC  below) is to find two points that are equidistant from the rays that create the angle (such as points   A and   D below).

anonymous · Answer

Medal?