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

Which statement best explains why Ben should not change the width of the compass while drawing the arcs at A and B from Q? (6 points)

Group of answer choices

∠AQS ≅ ∠BQS when lines QP and QR are equal.

∠AQS ≅ ∠BQS when segments AQ and BQ are equal.

∠AQS ≅ ∠BQS when angle ASQ is equal to angle BQS.

∠AQS ≅ ∠BQS when angle AQS is equal to angle BSQ.

option b is right

Step-by-step explanation:

Given that Ben uses a compass and a straightedge to bisect angle PQR,

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.

The purpose of taking equal width in the compass while drawing the arcs at A and B from Q are to get an isosceles triangle QAB so that by property of isosceles triangle we will have angle aqs = bqs

Hence out of the four options given I option is wrong because qp need not be equal to qr as per given statement

b) is right.

c) is wrong because asq why equal to bsp when arcs are equal is not justified

d is wrong aqs is equal to bsq is not explained properly

So option b is right