Question

select the correct answer.
image of angle construction
what needs to be corrected in the following construction for copying ∠abc with point d as the vertex?
a. the second arc should be drawn centered at k through a.
b. the second arc should be drawn centered at j through a.
c. the third arc should cross the second arc.
d. the third arc should pass through d.

Explanation:

Step1: Recall Angle Copying Construction

To copy an angle (e.g., \( \angle ABC \)) with a new vertex (e.g., \( D \)), the steps involve: 1) Drawing an arc centered at \( B \) intersecting \( BA \) and \( BC \) (at \( J \) and \( K \)). 2) Drawing an arc centered at \( D \) (same radius as first arc) intersecting \( DM \) (at \( L \)). 3) Drawing an arc centered at \( L \) with radius \( JK \) to intersect the second arc, then connecting \( D \) to the intersection.

Step2: Analyze Each Option

• Option A: The second arc should be centered at \( K \)? No, the second arc is centered at \( D \) (new vertex), not \( K \). Eliminate.
• Option B: The second arc centered at \( J \)? No, the second arc is centered at \( D \), not \( J \). Eliminate.
• Option C: The third arc (centered at \( L \)) must intersect the second arc (centered at \( D \)) to define the angle’s side. This matches the construction logic.
• Option D: The third arc passes through \( D \)? No, the third arc is centered at \( L \) to intersect the second arc, not pass through \( D \). Eliminate.

Answer:

C. The third arc should intersect the second arc.