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

Question

BQ = BS when ∠AQS ≅ ∠BQS. 

AQ = AS when ∠AQS ≅ ∠BQS.

 ∠AQS ≅ ∠BQS when AS = BS and AQ = BQ. 

∠AQS ≅ ∠BQS when AS = BQ and BS = AQ.

Answer 1

Statement 3.

It uses the theorem side/side/side between "triangles" AQS and BQS to show they're identical (not just similar). The triangle AQS has sides AQ, QS, and AS, and the triangle BQS has sides BQ, QS, and BS. When AQ = BQ and AS = BS, QS = QS since they're the same line, therefore, the angles ∠AQS and ∠BQS are identical, and they will have the same arc length with identical sides.