Question

2. Use only a compass and a straightedge to construct each
of the following, if possible:
a. A segment congruent to and an angle congruent
to ÚACB
CB

Answer 1

To construct a segment congruent to CB

set the compass to the length CB
Place the compass at a new point D
Draw an arc EF
Draw a line from D to any point G on the arc EF.
DG is congruent to CB.

Having the segment point D and arc EF,
Place the compass at B and set it to the length AB.
Place the compass at E and draw an arc that intersects arc EF at H.
Angle HDE is congruent to ACB.