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

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.

To construct a segment congruent to CB, follow these steps:

1. Take the compass and set the width to greater than half the length of CB.
2. Place the compass point on point C and draw an arc that intersects CB. Label one of the intersection points as D.
3. Without changing the width of the compass, place the compass point on point D and draw an arc that intersects the previous arc. Label the new intersection point as E.
4. Draw a straight line segment connecting C and E using a straightedge.

Now, to construct an angle congruent to �ÚACB, follow these steps:

1. Place the compass point on point C and draw an arc that intersects CA and CB. Label one of the intersection points as F.
2. Without changing the width of the compass, place the compass point on point F and draw an arc that intersects the previous arc. Label the new intersection point as G.
3. Place the compass point on point G and draw an arc that intersects the previous arc. Label the new intersection point as H.
4. Using a straightedge, draw a line segment connecting point G to point H.
5. Place the compass point on point G and draw an arc that intersects the line segment GH. Label the new intersection point as I.
6. Draw a straight line segment connecting point G and point I using a straightedge. This line segment will be congruent to angle �ÚACB.

Remember, when using a compass and a straightedge, it is not always possible to construct an exact congruence. In some cases, an approximation will be made.

To construct a segment congruent to CB, we will use a compass and a straightedge.

1. Start by drawing a line with two points A and B.
2. Place the compass on point C and adjust the width so that it reaches point B. Lock the compass at this width.
3. Without changing the width of the compass, place the compass on point A and draw a semi-circle that intersects the line created in step 1 at point D.
4. Using the straightedge, draw a line connecting points C and D.
The line segment CD is congruent to CB.

Now, let's move on to constructing an angle congruent to angle ACB.

1. Draw a line with two points A and B.
2. Place the compass on point C and draw an arc that intersects the line at two points, D and E.
3. Without changing the width of the compass, place the compass on D and draw an arc within the angle created by lines AD and CD.
4. Place the compass on E and draw an arc within the angle created by lines BE and CE.
5. Using a straightedge, draw a line connecting the two intersection points of the arcs created in steps 3 and 4.
The angle formed by the lines AD and BE is congruent to angle ACB.

Therefore, using a compass and a straightedge, you can construct a segment congruent to CB and an angle congruent to ACB.