Suppose that you are given line segment AB. Construct two circles-one centered at A with radius AB, and the other centered at B with radius BA. Let C and D denote the intersection points of these two circles. Draw the line segment CD. Mark the intersection of segments AB and CD as point E. Use congruent triangles to prove or disprove each of the following statements.

a. Triangle ABC and triangle ABD are equilateral.

b. E is the midpoint of segment AB.

c. E is the midpoint of segment CD.

d. AB is perpendicular CD

e. AB is congruent to CD

f. ACBD is a parallelogram

g. ACBD is a rhombus