Question

1. han followed these instructions to make the image.

a. given line j, mark 2 points on the line.
b. construct congruent circles a and b centered at the points on j.
c. construct line g through the intersection points of a and b.
d. construct circle c centered at 1 intersection point of a and b. mark the 2 intersection points of c and g.
e. construct congruent circles h and k centered at the points on g.
f. construct line l through the intersection points of h and k.
write a statement about each pair of lines in this construction. (3 statements)

Explanation:

Step1: Analyze line \(j\) and \(g\)

Line \(g\) is constructed as the perpendicular - bisector of the segment between the two points on line \(j\). So, line \(g\) is perpendicular to line \(j\).

Step2: Analyze line \(g\) and \(l\)

Line \(l\) is constructed in a similar perpendicular - bisector fashion with respect to points on line \(g\). So, line \(l\) is perpendicular to line \(g\).

Step3: Analyze line \(j\) and \(l\)

Since \(g\perp j\) and \(l\perp g\), line \(j\) is parallel to line \(l\) (two lines perpendicular to the same line are parallel).

Answer:

1. Line \(j\) is perpendicular to line \(g\).
2. Line \(l\) is perpendicular to line \(g\).
3. Line \(j\) is parallel to line \(l\).