Question

Construct a parallel line to DF through point F. Then, constrict a bisector to EDF that goes through the parallel line you just created.

Answer 1

The construction of a parallel line to DF through point F, uses a straightedge and compass construction. To construct a bisector of angle EDF that goes through the parallel line, follow the steps.

Step-by-step explanation:

To construct a parallel line to DF through point F, we can use a straightedge and compass construction. Here are the steps:

1. Draw a line segment DF.
2. Place the compass at point F and draw an arc that intersects line DF at two points.
3. Without changing the compass width, place the compass at one of the points where the arc intersects line DF and draw another arc.
4. Draw a line through point F and one of the points where the second arc intersects line DF. This line is parallel to line DF.

To construct a bisector of angle EDF that goes through the parallel line we just created, follow these steps:

1. Place the compass at point D and draw an arc that intersects the lines DE and DF.
2. Without changing the compass width, place the compass at point E and draw another arc that intersects the first arc at two points.
3. Draw a line through point E and one of the points where the arcs intersect. This line is the angle bisector of angle EDF that goes through the parallel line.