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?
O A.
B.
O C.
D.
OE.
When Jenna labeled the diameter, she should have named the endpoints F and G.
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.
When Jenna drew the arc that intersected circle C, she should have used point D as the center of the arc.
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.
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.

Answer 1

The correct answer is: 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.

In the construction of an equilateral triangle inscribed in a circle, the key step is to draw an arc centered at a point (E in this case) with a compass set to the radius of the circle. The radius is the distance from the center of the circle (O) to any point on the circumference (E).

If Jenna used the compass with a width smaller than the radius, the arc would not intersect the circle at two distinct points (F and G), resulting in an inaccurate construction.

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.

Answer 2

Jenna's first mistake was labeling the diameter endpoints as D and E; the correct method involves drawing arcs from both endpoints to find the equilateral triangle's vertices on the circle's circumference.

Step-by-step explanation:

The first error Jenna made in attempting to construct an equilateral triangle inscribed in circle C was when she labeled the endpoints of the diameter D and E. For an equilateral triangle inscribed within a circle, the vertices should be evenly spaced around the circle. The correct step after drawing the diameter would have been to use the compass set to the length of the radius to draw two arcs: first from point D and then from point E, finding two new points on the circumference where the two arcs intersect the circle. These intersection points should be labeled F and G, respectively. Jenna should have then used a straightedge to connect points E, F, and, G to form the equilateral triangle. Therefore, the correct answer to the question is:

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.