On her paper, Tonya wants to construct the angle bisector of PQR. She has drawn an arc from the vertex point Q that intersects both sides of the angle, and had 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?

Question

Option #1: Draw a line extending from the vertex point Q through the middle 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 side of the angle
Option #3: 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 #4: Place the pointed end of the compass on point P and draw another arc outside the first arc and between two side of the angle

Answer 1

To construct the angle bisector after labeling the intersections of the arc with the sides of the angle as points P and R, the 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 the two sides of the angle.

This step involves creating a new arc that intersects the previously drawn arc, which will help in finding the point where the angle bisector will pass through. After drawing the new arc from point P, you would then repeat the same process from point R, creating another arc that intersects the first new arc. The intersection of these two arcs will help you determine the direction of the angle bisector.