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 i through the intersection points of h and k.
write a statement about each pair of lines in this construction. (3 statements)
•line j contains two congruent circles, a and b.
•line g contains three points.
•line i was constructed by the intersection of points h and k.

Explanation:

Step1: Analyze line j and g

Line g is constructed as the perpendicular - bisector of the segment joining the centers of circles A and B (centered on j). So, line g is perpendicular to line j.

Step2: Analyze line g and i

Line i is constructed in a similar way as line g was constructed with respect to line j. Line i is perpendicular to line g.

Step3: Analyze line i and j

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

Answer:

• Line j and line g are perpendicular.
• Line g and line i are perpendicular.
• Line i and line j are parallel.