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 ∠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 ∠abc.
step 3: then, she placed the compass on point c and drew an arc on the interior of ∠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 ∠abc.

Explanation:

Step1: Analyze the correct process of constructing an angle bisector

To construct the angle bisector of \(\angle ABC\), after drawing an arc from \(B\) intersecting \(BA\) at \(D\) and \(BC\) at \(E\) (Step 1 is correct), the next step should be to place the compass on \(D\) and \(E\) (not \(D\) and \(C\)) to draw arcs that intersect.

Step2: Check each step

• Step 1: Correct as it is the initial step of marking points on the two - sides of the angle.
• Step 2: Placing the compass on \(D\) is a part of the correct process (but the radius should be appropriate).
• Step 3: Mistake! After step 2 (placing on \(D\)), the next should be placing on \(E\) (not \(C\)) to draw an arc.
• Step 4: Depends on the previous steps. Since step 3 is wrong, step 4 (if based on wrong arcs) will also be wrong, but the root - cause of the error is in step 3.

Answer:

Step 3