Question

Ben uses a compass and a straightedge to bisect angle PQR, as shown.

The figure shows two rays QP and QR having a common end point Q. An arc drawn from Q cuts the ray QP at A and the ray QR at B. Two small arcs intersect between the lines QP and QR. The point of intersection of the arcs is labeled S. The points Q, S, and T are joined with a line.

Which statement best explains why Ben uses the same width to draw arcs from A and B which intersect at S?

BQ = BS when angle AQS is congruent to angle BQS.

AQ = AS when angle AQS is congruent to angle BQS.

angle AQS is congruent to angle BQS when AS = BS and AQ = BQ.

angle AQS is congruent to angle BQS when AS = BQ and BS = AQ.