Question

a compass and straight edge construction is shown. which construction does the diagram illustrate? congruent segments perpendicular bisector angle bisector congruent angles

Explanation:

• Congruent segments: Construction would focus on equal - length line segments, not shown here.
• Perpendicular bisector: Involves bisecting a segment at a right - angle, not depicted.
• Angle bisector: The construction starts by drawing an arc from vertex \(A\) intersecting the sides of the angle at \(B\) and \(C\). Then, arcs are drawn from \(B\) and \(C\) (with the same radius) intersecting at \(X\). The line \(AX\) divides the angle at \(A\) into two equal parts, which is the definition of an angle - bisector construction.
• Congruent angles: Usually involves copying an angle, not the process shown.

Answer:

angle bisector