Question

using a compass and straightedge, construct the perpendicular bisector of ab. leave all construction marks. using a compass and straightedge, construct the bisector of the angle shown below. leave all construction marks.

Explanation:

Step1: Construct perpendicular bisector of line segment AB

1. Place the compass at point A and set the width to more than half the length of AB.
2. Draw arcs above and below the line segment AB.
3. Without changing the compass width, place the compass at point B and draw similar arcs above and below AB, intersecting the previous arcs at two points.
4. Use the straightedge to draw a line through the two intersection - points. This is the perpendicular bisector of AB.

Step2: Construct angle bisector

1. Place the compass at the vertex of the angle.
2. Draw an arc that intersects both rays of the angle at two distinct points.
3. From each of these two intersection points on the rays of the angle, draw arcs of the same radius inside the angle. These two arcs will intersect at a point.
4. Use the straightedge to draw a ray from the vertex of the angle through the intersection point of the two inner - arcs. This is the angle bisector.

Answer:

The perpendicular bisector of AB and the angle bisector are constructed as described above with all construction marks left.