Question

Jay is copying an angle. His work so far is shown below. Explain the importance of his next step, which is placing the point of the compass on L, opening the compass to N, and drawing an arc.

A. This ensures that when he draws another arc for angle Y, that it will be the right distance from point Z. <-- MY ANSWER


B. This arc is to make sure that both L and N are equidistant from M.


C. This arc makes sure that the distance from L to N is the same as the distance from Y to Z.


D. This way there will be two arcs drawn on both angles when he is done.

Answer 1

your answer is correct.

Explanation:

For the purpose here, we'll call the missing point on the arc through Z point X.

Essentially, you want to make ΔXYZ ≅ ΔLMN by SSS. The construction so far ensures LM ≅ MN ≅ XY ≅ YZ. By copying the length LN to XZ, you ensure the congruence of the remaining sides of the triangles.

Then ∠XYZ ≅ ∠LMN because corresponding parts of congruent triangles are congruent.

In short, XZ needs to be the same distance as LN.