Question

The steps below describe the construction of a line AG that is parallel to segment PQ and passes through a point A outside of PQ.

Step I
Step 2
Step 3

Which statement describes the next step?
a) The width of the compass is adjusted to DE, and an arc is drawn from Point E
b) The width of the compass is adjusted to DE, and an arc is drawn from Point A
c) The width of the compass is adjusted to DE, and an arc is drawn from Point F
d) The width of the compass is adjusted to DE, and an arc is drawn from Point D

Answer 1

The next step in constructing a line AG parallel to PQ is to adjust the compass to the width DE and then draw an arc from Point A.

Step-by-step explanation:

The student is trying to construct a line AG that is parallel to segment PQ. Given that the width of the compass should be adjusted to DE, the correct statement describing the next step is b) The width of the compass is adjusted to DE, and an arc is drawn from Point A. This is because once we have the correct width DE (which corresponds to the distance between points on lines PQ and AG that should be equidistant if AG is to be parallel to PQ), we use Point A as the center to draw an arc that will eventually intersect with a line from Point F, allowing us to draw line AG parallel to PQ through Point A.