Question

from unit 1, lesson 2
this diagram was created by starting with points
c and d and using only a straightedge and compass
to construct the rest. all steps of the construction
are visible.
select all the steps needed to produce this diagram.
a construct a circle centered at a.
b construct a circle centered at c.
c construct a circle centered at d.
d label the intersection points of the circles a and b.
e draw a line through points c and d.
f draw a line through points a and b.

Explanation:

• To create the diagram, we start with points \(C\) and \(D\). First, we construct circles centered at \(C\) and \(D\) (steps \(B\) and \(C\)) with the same radius (since the construction is with straight - edge and compass). Then, we find the intersection points \(A\) and \(B\) of these two circles. Finally, we draw the line through \(A\) and \(B\) (step \(F\)).
• Constructing a circle centered at \(A\) (\(A\)) is not a starting step as we start with \(C\) and \(D\). There are no circles centered at \(A\) and \(B\) in the initial construction steps shown. Labeling intersection points of \(A\) and \(B\) (\(D\)) is incorrect as \(A\) and \(B\) are intersection points of circles centered at \(C\) and \(D\). Drawing a line through \(C\) and \(D\) (\(E\)) is not part of the final diagram shown.

Answer:

B. Construct a circle centered at \(C\), C. Construct a circle centered at \(D\), F. Draw a line through points \(A\) and \(B\)