Question

Ben uses a compass and a straightedge to bisect angle PQR, as shown below: The figure shows two rays QP and QR with a common endpoint 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 that intersect at S? 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

Answer:

The correct option is;

∠AQS ≅ ∠BQS when AS = BS

Step-by-step explanation:

Given that AQ is equal to BQ. When AS is drawn congruent to BS, we have;

QS is congruent to SQ by reflective property

Therefore;

The three sides of triangle QAS are congruent to the three sides of triangle QBS, from which we have;

∠AQS and ∠BQS are corresponding angles, therefore;

∠AQS ≅∠BQS because corresponding angles of congruent triangles are also congruent.

Answer 2

Answer:

∠AQS ≅ ∠BQS when AS = BS and AQ = BQ

Step-by-step explanation: