Exercise 1A. Congruent Segments:
Compass center on endpoint

Finding the hole that is the same length

Draw Construction mark on original 
Draw ray LONGER than original segment

Using same hole as before mark the length of the segment

Put in other endpoint.
Part B draws another line of the same length from the second endpoint. 
Exercise 2: Equilateral Triangle

Draw an arc using one endpoint as center of the circle and other endpoint as the edge. 
Do a similar arc from the other endpoint.

Make sure the arcs cross

Connect one endpoint to the intersection of the arcs. 
Do the same from the other endpoint

All three segments are radii for congruent circles which means they themselves are congruent.

Exercise 3: Congruent Angles
Draw a one side of the new angle 
Draw an arc of ANY size on the first angle using the vertex as the center 
Draw an arc of the same size using the endpoint of the new angle as the center

Use the intersection of the arc and the side as the center and draw an arc that goes through the other intersection of arc and side.

Draw the same size arc on the new angle using the intersection of the arc and side as the center

Draw the second side from the endpoint to the intersection of the two arcs

A completed congruent angle

Exercise 4: Perpendicular Bisector
Draw an arc of any size using one endpoint as the center. (although the size of the segment works best) 
Draw an arc of the same size from the other endpoint

Connect the intersections of the arcs.

The resulting segment is both perpendicular to the segment and divides it into equal parts.

Exercise 5: Bisecting an Angle
Draw an arc of any size using the vertex as a center 
Draw an arc of any size* using the intersection of the first arc and a side as the center.

Repeat this arc from the other intersection of side and arc.

Draw a line from the vertex through the intersections of the two arc that cross.

Resulting line bisects the angle.
*If the second and third arc do not intersect you must make them larger. 