Question

Maggie is making an exact copy of angle ∠n on the ray SW First, she drew the arc, centered at N, through P and H. Then, she located point L so that SL=NH. Next, she drew the arc, centered at point L, with radius PH. What must be true?

A) ∠NHL is congruent to ∠N.

B) ∠SLH is congruent to ∠N.

C) ∠SLH is congruent to ∠NHL.

D) ∠NHL is congruent to ∠SLH.

Answer 1

Maggie copied angle ∠N successfully onto ray SW by drawing congruent arcs and thus ∠SLH is congruent to ∠N.

Step-by-step explanation:

To answer the question of what must be true after Maggie attempts to copy angle ∠n on the ray SW, we need to review the steps she took. First, she drew an arc with center N through points P and H. Then, she found a point L such that SL is equal to NH, and subsequently, she drew another arc centered at L with radius equal to PH.

Given these actions, the result will be that ∠SLH is congruent to ∠N. The process Maggie has used is the standard way to replicate an angle using a compass and straightedge. She correctly transferred the length of the arc NH to arc SL, and by using the same radius PH to draw the arc centered at L, the angles subtended by the two arcs (NH and SL) will be congruent.

Therefore, the correct answer is B) ∠SLH is congruent to ∠N.