Question

which of the following shows the construction of an angle bisector?

Explanation:

To determine the angle bisector construction, recall the steps: 1. Draw an arc from the vertex intersecting both sides. 2. From each intersection, draw arcs of equal radius inside the angle, intersecting at a point. 3. Draw a line from the vertex to this intersection (the bisector).

• The first (yellow) diagram: Has an arc from vertex \( P \) intersecting both sides, then an arc from those intersections meeting at \( W \), with \( PW \) as the bisector. This matches angle - bisector construction steps.
• The second (purple) diagram: Shows parallel - line or vertical - angle construction, not angle bisector.
• The third (orange) diagram: Just arcs on angles without the bisector - forming intersection, not a bisector construction.
• The fourth (teal) diagram: Is a perpendicular bisector of a segment (\( AB \)), not an angle bisector.

Answer:

The first (yellow - colored) diagram (with vertex \( P \), arcs intersecting sides, and a line \( PW \) as the bisector) shows the construction of an angle bisector.