MATH SOLVE

4 months ago

Q:
# Lisa is constructing an equilateral triangle. She used a straightedge to draw a segment and labeled the endpoints of the segment G and H.Which move is a correct second step?With the compass point halfway between points G and H, open the compass until the pencil point is halfway to G and draw a circle.With the compass point halfway between points G and H, open the compass until the pencil point is on G and draw a circle.With the compass point on G, open the compass until the pencil point is on H and draw a circle.With the compass point on G, open the compass until the pencil point is on the segment, closer to point H than to point G, and draw a circle.

Accepted Solution

A:

With the compass point on G, open the compass until the pencil point is on H and draw a circle.
Since Lisa is wanting an equilateral triangle, she's going to want draw 2 circles who's radius is the distance between points G and H. The center of one circle will be at G and the other at H. Then she simply needs to draw a line from G to an intersection of the two previously drawn circles and another line from H to the same intersection. With the above description in mind, let's look at the options and see if anything matches.
With the compass point halfway between points G and H, open the compass until the pencil point is halfway to G and draw a circle.
* This option involves a lot of guess work that can't be accomplished. How does she know a "point halfway between points G and H"? Then how does she open the compass to "halfway to G". So this is a bad choice.
With the compass point halfway between points G and H, open the compass until the pencil point is on G and draw a circle.
* Move guesswork involved here. So it's a bad choice.
With the compass point on G, open the compass until the pencil point is on H and draw a circle.
* Nice precise instructions that use known specified points. And it happens to match the drawing of the circles mentioned above in my description. So this is the correct choice.
With the compass point on G, open the compass until the pencil point is on the segment, closer to point H than to point G, and draw a circle.
* More fuzzy guesswork. So this is a bad choice.