Question

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:

⚡ Using what you learned: Justifying Constructions and Properties

Step 1: Analyze the standard angle bisector construction

To construct the angle bisector of \(\angle ABC\):

1. Place the compass point on the vertex \(B\) and draw an arc intersecting ray \(BA\) at some point \(D\) and ray \(BC\) at some point \(E\). This ensures \(BD = BE\).
2. Place the compass point on the intersection point \(D\) and draw an arc in the interior of the angle.
3. Keep the same compass width (or adjust it, but keep it consistent for both points), place the compass point on the other intersection point \(E\) (not the original point \(C\)), and draw an arc intersecting the previous arc.
4. Label the intersection of these two arcs as \(F\), and draw ray \(BF\).

Step 2: Identify the mistake in the given steps

Let's compare the standard steps with the student's actions:

• 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 \(E\)." (Correct)
• Step 2: "Next, she placed the compass on point \(D\) and drew an arc on the interior of \(\angle ABC\)." (Correct)
• 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." (Incorrect)

The mistake is in Step 3. She placed the compass on point \(C\) instead of the intersection point \(E\) on ray \(BC\).

Answer:

Step 3