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 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
.
Line segment Modifying above upper Q upper C with bar is the angle bisector of angle upper P upper Q upper R .

Line segment QP¯¯¯¯¯¯¯¯
s the angle bisector of ∠PQR
.

Answer 1

To determine which line segment is the angle bisector of ∠PQR, we need to locate the segments given and analyze how angle bisectors work.

An angle bisector divides an angle into two equal angles.

• Segment AC would be an angle bisector if it splits ∠PQR into two angles of equal measure.
• Segment BR would be an angle bisector if it splits ∠PQR into two angles of equal measure.
• Segment QC would similarly need to split ∠PQR into two equal angles.
• Segment QP would also serve as an angle bisector if it divides the angle equally.

Without the specific image to reference which segment is exactly bisecting the angle, it is not possible to definitively state which line segment is the angle bisector.

However, if segment AC is the line drawn from Q to C and it visually divides the angle PQR into two equal halves, then it would be the angle bisector.

Please identify or describe any visual or spatial relationships in the diagram that would indicate how these segments are related to the angle they form. If you can confirm that one of these segments divides the angle into two equal parts, that would be considered the angle bisector.