Question

1. construct the bisector of ∠a.

Explanation:

Step1: Open compass at A

Set compass width to draw arcs on both sides of \( \angle A \), intersecting \( AB \) and \( AC \) at two points (say \( D \) on \( AB \), \( E \) on \( AC \)).

Step2: Arc from D and E

With same compass width, draw arcs from \( D \) and \( E \) inside \( \angle A \), intersecting at point \( F \).

Step3: Draw angle bisector

Draw ray \( AF \) from \( A \) through \( F \). \( AF \) bisects \( \angle A \).

Answer:

The angle bisector of \( \angle A \) is constructed by drawing a ray from \( A \) that splits \( \angle A \) into two equal angles (using compass - and - straightedge construction steps as above). Visually, it is the ray from \( A \) towards the intersection of the arcs drawn from points on \( AB \) and \( AC \).