Question

topic: constructions with compass and straight edge.

1. use a compass and a straightedge to bisect the angle. check your construction by folding the paper.

Explanation:

Step1: Open the compass to a suitable radius

With \( B\) as the center, draw an arc that intersects \( BA\) and \( BC\), let the intersection points be \( D\) and \( E\) respectively.

Step2: Open the compass to a radius greater than \(\frac{1}{2}DE\)

With \( D\) and \( E\) as centers respectively, draw arcs inside the angle \( \angle ABC\). Let the intersection point of these two arcs be \( F\).

Step3: Draw the ray \( BF\)

The ray \( BF\) is the bisector of \( \angle ABC\).

Answer:

The ray \( BF\) bisects \( \angle ABC\).