Question

construct ∠d so that ∠d ≅ ∠c. assume ∠c has already been constructed. what is the first step to construct ∠d?
a. plot points c and d and draw a ray through them using c or d as an endpoint.
b. draw a ray and label the endpoint d.
c. draw a segment with endpoints c and d.
d. plot points c and d and draw a line through them.
what is the second step in the construction?
a. with the compass point on d, draw an arc that intersects the sides of ∠c. label these points of intersection a and b.
b. open the compass to length cd.
c. with the compass point on c, draw an arc that intersects the construction in the previous step. label the intersection q.
d. with the compass point on c, draw an arc that intersects the sides of ∠c. label these points of intersection a and b.

Explanation:

First Question (Multiple Choice)

To construct an angle congruent to \( \angle C \) (i.e., \( \angle D \cong \angle C \)), the first step is to create a ray with endpoint \( D \) (the vertex of the new angle). Option A involves points \( C \) and \( D \), which is not necessary initially. Option C draws a segment, not a ray for the angle. Option D draws a line, but we need a ray for the angle's side. Option B correctly starts by drawing a ray with endpoint \( D \) to begin constructing \( \angle D \).

After drawing the ray with endpoint \( D \) (first step), the next step in constructing \( \angle D \cong \angle C \) is to copy the arc from \( \angle C \). To do this, we first draw an arc on \( \angle C \) with the compass point at \( C \), intersecting its sides (labeled \( A \) and \( B \)). Option A has the compass on \( D \) too early. Option B opens to length \( CD \), which is irrelevant. Option C uses the compass on \( C \) but refers to a previous construction step (the ray at \( D \)) which is not the correct order. Option D correctly describes drawing an arc on \( \angle C \) to get the angle's "width" for copying.

Answer:

B. Draw a ray and label the endpoint D.

Second Question (Multiple Choice)