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 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.

Answer 1

To identify the angle bisector of ∠PQR, we need to understand the configuration of points and lines mentioned.

In the setup:

• Q is the vertex of the angle ∠PQR.
• P and R lie on lines that diverge from point Q.
• C is a point on the line between P and R.

An angle bisector in geometry is a line that divides an angle into two equal angles. Thus, to determine the angle bisector of ∠PQR, we need to see which line segment is positioned such that it creates two equal angles between the segments QP and QR.

In this case, the line segment QC appears to connect point Q with point C, which is located on the angle's interior. Typically, in such configurations, the segment that touches the angle's interior and connects to the vertex is the angle bisector. Hence, segment QC would divide ∠PQR into two equal parts.

Therefore, the answer is:

Line segment QC is the angle bisector of ∠PQR.