Which step is the same in the construction of parallel lines and the construction of a perpendicular line through a point on the line?
a. create only one arc that intersects the original line.
b. create two arcs that intersect the original line.
c. place the compass on a point off the original line.
d. place the compass on a point on the original line.

"Place the compass on a point on the original line" ⇒ answer D

Step-by-step explanation:

* Lets revise the steps of constructing parallel lines and a

 perpendicular line through a point on the line

# Contracting parallel lines

- Given: Line AB and point P not on AB

1. Draw a slant line through point P and intersects AB at point C, this

  line is the transversal of the parallel lines

2. Place the pin of the compass at point C and draw an arc intersects

   AB at D and CP at E

3. Without changing the distance of the compass put the pin of the

   compass on point P and draw an arc intersects CP at point Q

4. Use the compass to measure the distance from D to E and place

   the pin of the compass at point Q and draw an arc intersects the

   arc from P to CP at point U

5. Join P and U by a line this line is parallel to AB

# Constructing a perpendicular line through a point on the line

- Given line AB and point P lies on it

1. Place your compass pin at P and draw an arc of any size below

  AB that crosses the line twice at points C and D

2. Stretch the compass to a larger distance

3. Place the compass pin on point C and draw a small arc above

   the line

4. Without changing the distance of the compass place the

   compass pin on point D and draw another arc intersects the arc

   from C at point E

5. Using a straightedge, join P and E where PE is perpendicular to AB

* Lets find the same steps in the constructions

∵ In first construction we put the pin of the compass at point C which

  lies in the original line AB

∵ In second construction we put the pin of the compass at point P

  which lies in the original line AB

∴ The common step is:

  "Place the compass on a point on the original line"

place the compass on a point on the original line

Step-by-step explanation: