Question

select the correct answer.
jenna attempted to construct equilateral triangle efg inscribed in circle c.
first, she used a compass to draw circle c and labeled its center. next, she used a straightedge to draw a diameter of the circle. she labeled the
endpoints of the diameter d and e. then, keeping the compass set equal to the radius of circle c, she drew an arc centered at point e, which
intersected the circle at two points that she labeled f and g. finally, she used a straightedge to draw three chords connecting points e, f, and g.
what was the first error jenna made in her construction?
a. when jenna labeled the diameter, she should have named the endpoints f and g.
b. when jenna drew the arc centered at point e, she should have changed the width of the compass to be less than the radius length.
c. when jenna drew the arc that intersected circle c, she should have used point d as the center of the arc.
d. when jenna labeled f and g, she should have only labeled f and then drawn a second arc centered at point d to find g.
e. when jenna drew the arc centered at point e, she should have changed the width of the compass to be greater than the radius length.

Explanation:

Step1: Analyze option A

When labeling the diameter endpoints \(F\) and \(G\), it's a correct initial step in constructing an inscribed equilateral triangle. So this is not the first - error.

Step2: Analyze option B

When drawing an arc centered at \(E\) (a diameter endpoint), the compass width should be equal to the radius (not less than the radius) of the circle to get the correct intersection points for an equilateral - triangle construction. This is an error.

Step3: Analyze option C

The arc that intersects circle \(C\) should be centered at \(D\) (the other diameter endpoint) not \(D\) as the center for the arc when centered at \(E\)'s related arc. But this is not the first error.

Step4: Analyze option D

Labeling \(F\) and \(G\) first and then using arcs centered at \(D\) (after proper arc - width setting) is a later step.

Step5: Analyze option E

Changing the compass width when centered at \(E\) (if the initial width was wrong) is a correction for a prior (option B) error.

Answer:

B. When Jenna drew the arc centered at point E, she should have changed the width of the compass to be less than the radius length.