The task in the image involves constructing angle bisectors and perpendicular lines. Below are the step-by-step instructions to complete the tasks:

1. Construct the angle bisectors of each angle shown below. Leave all construction marks.

(a) For the right angle $\angle A$:

1. Place the compass point on the vertex $A$.
2. Draw an arc that intersects both sides of the angle at two points.
3. Without changing the compass width, place the compass point on each intersection point and draw two arcs that intersect each other inside the angle.
4. Draw a straight line from $A$ through the point of intersection of the arcs. This is the angle bisector.

(b) For the angle $\angle S$:

1. Repeat the same steps:
   • Draw an arc from the vertex $S$ that intersects the two sides of the angle.
   • Place the compass point on the intersection points of the arc and the sides, and draw arcs that intersect inside the angle.
   • Connect $S$ to the intersection of these arcs to construct the angle bisector.

2. Construct the line perpendicular to the ones shown through the marked point on the line.

(a) Line $m$ through point $E$:

1. Place the compass point on $E$, and draw an arc that intersects line $m$ at two points on either side of $E$.
2. Place the compass point on each intersection point and draw two arcs above and below $E$. These arcs should intersect.
3. Draw a straight line through $E$ and the intersection of the arcs. This line is perpendicular to $m$.

(b) Line $n$ through point $L$:

1. Repeat the same steps:
   • Place the compass point on $L$, and draw an arc that intersects line $n$ at two points.
   • From these intersection points, draw two arcs that intersect each other above or below $L$.
   • Draw a line through $L$ and the intersection of these arcs. This line is perpendicular to $n$.

Would you like further clarification or diagrams to accompany these instructions?

Questions for further exploration:

1. How is the method for constructing a perpendicular bisector different from constructing an angle bisector?
2. Why are construction marks important when performing geometric constructions?
3. Can you identify real-world applications of constructing perpendicular lines and angle bisectors?
4. How would you construct an angle of 60° using only a compass and straightedge?
5. How can the accuracy of constructions be ensured when using a compass and straightedge?

Tip:

Always ensure the compass width is consistent during each construction step to maintain accuracy.