Use the image to answer the question.

Question

Three lines diverge from vertex point upper Q. Points marked on the ends of the top and bottom lines are labeled upper P and upper R, respectively. A point marked on the right side of the middle line is labeled upper C.

Laci constructed ∠PQR
with line segments QC¯¯¯¯¯¯¯¯
, AC¯¯¯¯¯¯¯¯
, and BC¯¯¯¯¯¯¯¯
, as shown in the image. Which line segment is the angle bisector of ∠PQR
?

(1 point)
Responses

Line segment QP¯¯¯¯¯¯¯¯
s the angle bisector of ∠PQR
.
Line segment Modifying above upper Q upper P with bar s the angle bisector of angle upper P upper Q upper R .

Line segment AC¯¯¯¯¯¯¯¯
is the angle bisector of ∠PQR
.
Line segment Modifying above upper A upper C with bar is the angle bisector of angle upper P upper Q upper R .

Line segment BR¯¯¯¯¯¯¯¯
is the angle bisector of ∠PQR
.
Line segment Modifying above upper B upper R with bar is the angle bisector of angle upper P upper Q upper R .

Line segment QC¯¯¯¯¯¯¯¯
is the angle bisector of ∠PQR
.

Answer 1

To determine which line segment is the angle bisector of ∠PQR, we need to recall that an angle bisector divides the angle into two equal parts.

Considering the options given:

• If line segment QP were the angle bisector, it would have to split ∠PQR into two equal angles. However, it is one of the sides of the angle.
• The line segment AC appears to be a straight segment drawn from a point C on the line QR that could potentially bisect the angle.
• Similarly, BR and QC would only be bisectors if they created two equal angles, which needs further context from the image.

Since we would need to identify which line segment actually bisects the angle based on the configuration depicted in the image, it seems likely that line segment AC is specifically constructed in the context to state it is the angle bisector.

Therefore, the most plausible response would be: Line segment AC is the angle bisector of ∠PQR.