Question

construct the bisector of ∠a.

Explanation:

Step1: Use the Circle tool

With center at \( A \), draw a circle (arc) that intersects both sides of \( \angle A \) (the two rays) at points, say, \( B \) (already on one ray) and a new point on the other ray (let's call it \( D \)) such that \( AB = AD \).

Step2: Use the Circle tool again

With center at \( B \) and radius equal to the distance from \( B \) to \( D \) (or a suitable radius), draw an arc inside \( \angle A \). Then, with center at \( D \) and the same radius, draw another arc that intersects the previous arc at a point \( E \).

Step3: Use the Ray tool

Draw a ray from \( A \) through \( E \). This ray \( AE \) is the angle bisector of \( \angle A \), as it divides \( \angle A \) into two equal angles by the construction of congruent triangles (SSS congruence: \( AB = AD \), \( BE = DE \), \( AE = AE \)).

Answer:

The angle bisector of \( \angle A \) is constructed by drawing a ray from \( A \) through the intersection point of the two arcs (as per the steps above), dividing \( \angle A \) into two equal angles. (Note: Since this is a construction problem, the final answer is the constructed angle bisector ray, typically represented as a ray from \( A \) towards the interior of \( \angle A \) that splits it equally.)