Constructions 1 - Duplicating Segments and Angles

In order to duplicate a segment:

Create a Segment longer than the segment you are duplicating
Measure the Original segment with the Compass tool (either click the segment, or each endpoint)
Click on one of the endpoints of the Segment you created in step 1 (to set that as the center of the circle you're creating with the Compass)
Mark the Point the Circle intersects the segment from step 1.
Create a Segment connecting the points from steps 3 and 4

Duplicate Segment AB

To Duplicate an Angle:

Create a Segment.
Add a Point to any side of the angle.
Use the Compass to draw a circle going through that point with center at the vertex of the angle.
Add a Point where the circle and other side of the angle Intersect.
Copy the circle (from step 3) and place the center at an endpoint of the segment (from step 1).
Create a Point at the Intersection of the Segment (from step 1) and the Circle (from step 5).
Use the Compass to draw a circle with the point from step 4 on it and with center at the point from step 2
Copy the circle from step 7 but make the center the point from step 6.
Create a Point at the Intersection of the circles from steps 5 and 8.
Create a Segment starting at the Point you picked in step 5 and the point from step 9.