Laci constructed ∠PQR

Question

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 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 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 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 .
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Answer 1

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

Given the segments:

• QC (from point Q to point C)
• AC (from point A to point C)
• BC (from point B to point C)
• QP (from point Q to point P)

Without the visual representation of the image, I cannot definitively say which line segment bisects the angle. However, typically:

• The angle bisector of ∠PQR will be the line segment that originates from point Q and points towards the interior of the angle formed by lines PQ and QR.

If it is clear from your image that one of the segments (e.g., QC or QP) is indeed dividing ∠PQR into two equal angles, that segment would be the angle bisector.

Here are the likely candidates for being the angle bisector based on common constructions:

• Line segment QC might be the bisector if it divides the angle ∠PQR into two equal angles at Q.
• If QP is inside the angle and divides it equally, then QP would be the angle bisector.

Please refer to your diagram to find out which segment fits this description. If I had to choose based on convention, I would tend toward suggesting line segment QP as the most likely angle bisector of ∠PQR, assuming it bisects the angle at Q. If you see it visually bisecting the angle, that would confirm it.

So, an appropriate response could be:

Line segment QP is the angle bisector of ∠PQR.