Question

1. construct a line perpendicular to line l, through point f.
2. construct the perpendicular bisector of $overline{pq}$.
3. construct the bisector of $angle cde$.
4. construct a line parallel to line p, through point m.

Explanation:

Step1: Construct perpendicular through point F to line l

1. Place the compass on point F.
2. Draw arcs that intersect line l at two points, say A and B.
3. Place the compass on A and draw an arc above (or below) the line l.
4. Without changing the compass width, place the compass on B and draw another arc that intersects the previous arc. Let the intersection point be C.
5. Draw the line FC. This is the line perpendicular to l through F.

Step2: Construct perpendicular - bisector of $\overline{PQ}$

1. Place the compass on point P and set the width to more than half of the length of $\overline{PQ}$.
2. Draw arcs above and below the line segment $\overline{PQ}$.
3. Without changing the compass width, place the compass on point Q and draw similar arcs that intersect the previous ones. Let the intersection points of the arcs be M and N.
4. Draw the line MN. This is the perpendicular - bisector of $\overline{PQ}$.

Step3: Construct angle - bisector of $\angle CDE$

1. Place the compass on point D.
2. Draw an arc that intersects the rays $\overrightarrow{DC}$ and $\overrightarrow{DE}$ at points G and H respectively.
3. Place the compass on G and draw an arc inside the angle.
4. Without changing the compass width, place the compass on H and draw another arc that intersects the previous arc. Let the intersection point be I.
5. Draw the ray $\overrightarrow{DI}$. This is the bisector of $\angle CDE$.

Step4: Construct parallel line to line p through point M

1. Place the compass on a point on line p, say K.
2. Draw an arc that intersects line p at K and another point, say L.
3. Without changing the compass width, place the compass on point M and draw a similar arc.
4. Measure the distance between K and L with the compass.
5. Place the compass on the intersection of the arc drawn from M and mark a point on the arc such that the distance between the two intersection points on the arc (from M) is the same as the distance between K and L. Let this point be N.
6. Draw the line through M and N. This is the line parallel to line p through point M.

Answer:

1. For constructing a line perpendicular to line l through point F: Follow the steps above to get the perpendicular line FC.
2. For constructing the perpendicular - bisector of $\overline{PQ}$: Follow the steps above to get the line MN.
3. For constructing the bisector of $\angle CDE$: Follow the steps above to get the ray $\overrightarrow{DI}$.
4. For constructing a line parallel to line p through point M: Follow the steps above to get the line through M and N.