The first step in constructing an angle bisector using a compass and straightedge is to start with your given angle. Let’s denote this angle as ∠ABC, where B is the vertex of the angle. Follow these steps:
1. **Place the Compass Point:** Position the compass point at the vertex of the angle, point B.
2. **Draw an Arc:** With the compass set to a comfortable width, draw an arc that intersects both sides of the angle (the lines AB and BC). Let the points where the arc intersects these lines be labeled as D (on line AB) and E (on line BC).
This arc serves as the foundational step in the angle bisector construction. The points D and E will be instrumental in finding the bisector in the subsequent steps. So once you have completed this step, you are set to proceed with the next stages of angle bisection!