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 QC¯¯
is the angle bisector of ∠PQR
.
Line segment Modifying above upper Q 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 AC¯¯
is the angle bisector of ∠PQR
.

Answer 1

To determine which line segment is the angle bisector of ∠PQR, we need to analyze how angle bisectors work. An angle bisector divides the angle into two equal parts.

In the options given:

1. Line segment \( \overline{QP} \) is directly between points P and Q, and does not divide the angle ∠PQR.
2. Line segment \( \overline{QC} \) is the segment from Q to C on the middle line. It may divide ∠PQR into two equal angles, making it a candidate for the angle bisector.
3. Line segment \( \overline{BR} \) does not apply as it connects point B to point R, which is not related to angle ∠PQR.
4. Line segment \( \overline{AC} \) is not relevant for angle ∠PQR, as it starts from a different point (A).

Given this information, the line segment that most likely serves as the angle bisector of ∠PQR is:

Line segment \( \overline{QC} \) is the angle bisector of ∠PQR.