Ben uses a compass and a straightedge to bisect angle PQR, as shown below: 1.8 units
3.5 units
4.99 units
5.82 units

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 w

Step-by-step explanation:

this is not the answer this is just a question. is this middle school math?

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.