On her paper, Katarzyna wants to construct the angle bisector of angle ∠PQR

Question

. She has drawn an arc from the vertex point Q
that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P
and R
. Using a compass and straightedge, what next step must she take to construct the angle bisector?

Option #1: Move the compass further apart and place the pointed end at point Q
and draw another arc that intersects the sides of the angle.

Option #2: Place the pointed end of the compass on point P
and draw another arc inside the first arc and between two sides of the angle.

Option #3: Place the pointed end of the compass on point P
and draw another arc outside the first arc and between two sides of the angle.

Option #4: Draw a line extending from the vertex point Q
through the middle of the angle.

(1 point)
Katarzyna’s next step is Option #
.
Remaining Attempts : 3
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Answer 1

To construct the angle bisector of angle ∠PQR after drawing the initial arc that intersects the sides of the angle at points P and R, Katarzyna should follow these steps:

1. With the compass pointed at point P, she should draw another arc that intersects the previous arc and segments PQ and QR.
2. Then, she should also do the same from point R, thus creating two new intersection points with the previous arcs.

This approach allows her to find points that will define the angle bisector. Therefore, the correct next step for Katarzyna would be:

Option #2: Place the pointed end of the compass on point P and draw another arc inside the first arc and between the two sides of the angle.

This step is crucial for defining points that will ultimately help her construct the angle bisector.