Question

7 problem 6
han followed these instructions to make the image.
a. given line j, mark 2 points on the line.
b. construct congruent circles, circle a and b, centered at the points on j.
c. construct line g through the intersection points of circles a and b.
d. construct circle c centered at 1 intersection point of circles a and b. mark the 2 intersection points of circle c and line g.
e. construct congruent circles, circles h and k centered at the points on line g.
f. construct line i through the intersection points of circles h and k.
write a statement about each pair of lines in this construction. (3 statements)

Explanation:

Step1: Analyze line j and g

When congruent circles A and B are centered at points on j and line g is drawn through their intersection - points, line g is the perpendicular bisector of the segment joining the centers of A and B (points on j). So, line g is perpendicular to line j.

Step2: Analyze line g and i

When congruent circles H and K are centered at points on g and line i is drawn through their intersection - points, line i is the perpendicular bisector of the segment joining the centers of H and K (points on g). So, line i is perpendicular to line g.

Step3: Analyze line j and i

Since line g is perpendicular to line j and line i is perpendicular to line g, line j is parallel to line i.

Answer:

1. Line j is perpendicular to line g.
2. Line i is perpendicular to line g.
3. Line j is parallel to line i.