Question

select the correct step in the table.
nikita began with the figure shown.
she completed the following actions to construct the angle bisector of \\( \angle abc \\), but made a mistake in one of the steps. select the step in which her mistake was made.

step 1: she placed the compass on point b and drew an arc which intersects ray ba at point d and ray bc at point e.
step 2: next, she placed the compass on point d and drew an arc on the interior of \\( \angle abc \\).
step 3: then, she placed the compass on point c and drew an arc on the interior of \\( \angle abc \\), which intersects the previous arc.
step 4: she labeled the intersection of the two arcs as point f and drew the ray bf, which represents the angle bisector of \\( \angle abc \\).

Explanation:

Step1: Analyze the correct method of constructing an angle bisector

When constructing an angle bisector of \(\angle ABC\):

• Step 1: Place the compass on point \(B\) and draw an arc intersecting \(BA\) at \(D\) and \(BC\) at \(E\). This is correct as it creates two points equidistant from \(B\) on the two sides of the angle.
• Step 2: Place the compass on point \(D\) and draw an arc on the interior of \(\angle ABC\). This is a correct step in the construction process.
• Step 3: The error occurs here. After drawing an arc from \(D\), the next arc should be drawn from point \(E\) (not \(C\)) with the same compass - width. The intersection of the arcs from \(D\) and \(E\) will give a point on the angle bisector.
• Step 4: If the previous steps were correct (using \(E\) instead of \(C\) in Step 3), then drawing the ray from \(B\) through the intersection point would be the angle bisector.

Answer:

Step 3