Question

what is the first step when constructing an angle bisector using only a compass and a straightedge?
a. place the compass needle on one of the legs of the angle, and draw an arc intersecting the other leg.
b. mark a point outside the angle, and draw an arc centered at the point, intersecting the vertex of the angle.
c. mark a point outside the angle, and draw a ray in any direction from the point.
d. place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.
e. mark a point in the angles interior, and draw an arc centered at the point, intersecting both legs of the angle.

Explanation:

To construct an angle bisector with a compass and straightedge, the first step is to place the compass needle on the vertex of the angle and draw an arc that intersects both legs. This is because the angle bisector construction starts by creating two intersection points on the angle's legs from the vertex. Option A starts on a leg, not the vertex. Options B, C, and E involve points outside or inside the angle initially, which is not the first step. Option D correctly describes the first step: placing the compass on the vertex and drawing an arc across both legs.

Answer:

D. Place the compass needle on the vertex of the angle, and draw an arc across both legs of the angle.