Trey takes the angle shown, places the point of his compass on S, and draws an arc with an arbitrary radius intersecting the rays of the angle at P and R. Trey claims that as long as he draws two more arcs by placing the needle of his compass on P and then on R, drawing a ray from S through the point at which the arcs intersect, he will be able to bisect ∠S. Is Trey correct? Explain.

Question

Trey takes the angle shown, places the point of his compass on S, and draws an arc with an arbitrary radius intersecting the rays of the angle at P and R. Trey claims that as long as he draws two more arcs by placing the needle of his compass on P and then on R, drawing a ray from S through the point at which the arcs intersect, he will be able to bisect ∠S. Is Trey correct? Explain.

(1 point)
Responses

Trey is correct. Since the initial arc was drawn with the point of the compass on S, RS=PS.
Trey is correct. Since the initial arc was drawn with the point of the compass on upper s , upper r upper s equals upper p upper s .

Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from P and R.
Trey is not necessarily correct. He will need to ensure that the compass width remains the same for each arc drawn from upper p and upper r .

Trey is correct. Since the compass is placed on the points P and R to draw the remaining two arcs, the ray drawn through their intersection will bisect the angle.
Trey is correct. Since the compass is placed on the points upper p and upper r to draw the remaining two arcs, the ray drawn through their intersection will bisect the angle.

Trey is not necessarily correct. He will need to ensure that the distance from S to P and the distan

Answer 1

Trey is not necessarily correct. He needs to be sure that the arcs drawn from P and R do in fact intersect -- that is, that the compass is open wider than 1/2 the distance PR.

Answer 2

Correct, Trey is not necessarily correct. In order for the bisecting ray to pass through the intersection of the arcs drawn from P and R, the compass width needs to be wider than half the distance PR. If the compass width is narrower than that, the arcs may not intersect and Trey would not be able to bisect the angle accurately.

Answer 3

Trey is not necessarily correct. He needs to be sure that the arcs drawn from P and R do in fact intersect -- that is, that the compass is open wider than 1/2 the distance PR.

ce from S to R are equal for the bisecting ray to pass through their intersection.