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

Question

∠
𝑃
𝑄
𝑅
. She has drawn an arc from the vertex point Q
𝑄
that intersects both sides of the angle and has labeled the intersection of the arc with the sides of the angle with P
𝑃
and R
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
𝑄
and draw another arc that intersects the sides of the angle.

Option #2: Place the pointed end of the compass on point P
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
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
𝑄
through the middle of the angle.

(1 point)
Katarzyna’s next step is Option #.

Answer 1

Katarzyna’s next step is 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.

This step will allow her to create two intersection points along the angle’s sides which will be used to find the angle bisector. After this arc is drawn, she will repeat the process from point R to locate the second intersection point, which will then help her to draw the angle bisector.