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 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 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
.

Answer 1

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

In the options given, the angle segments are:

1. Line segment QC (the middle line to point C)
2. Line segment BR (bottom line to point R)
3. Line segment QP (top line to point P)
4. Line segment AC (another segment related to the configuration)

Without the image, we generally rely on the properties of angle bisectors. The angle bisector typically stems from the vertex (in this case, point Q) and extends into the angle formed by the other two lines (QP and QR).

If line segment QC extends from point Q to point C and is positioned in such a way that it divides the angle ∠PQR into two equal angles, then it would be the angle bisector of ∠PQR.

Thus, if line segment QC is the one that goes from Q to C and is placed appropriately according to the angle divided by points P and R, we can conclude that:

Line segment QC is the angle bisector of ∠PQR.