Question

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 o.
○ 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.
what is the third step of the construction?
○ a. open the compass to length ab and put the compass point on c. draw an arc and label its point of intersection with the construction in the first step as r.
○ b. open the compass to length ab and put the compass point on d. draw an arc and label its point of intersection with the construction in the first step as r.
○ c. with the same compass setting, put the compass point on d. draw an arc and label its point of intersection with the construction in the first step as r.
○ d. with the same compass setting, put the compass point on c. draw an arc and label its point of intersection with the construction in the first step as r.

Explanation:

First Question (First Step to Construct ∠D)

To construct an angle equal to ∠C (∠D), the first step is to create a starting ray for ∠D. Drawing a ray with endpoint O gives the base for constructing the angle, which matches option B. Options A, C, D involve points C and D in ways not relevant to starting the angle construction for ∠D.

After having the ray for ∠D (endpoint O), the next step in copying ∠C is to mark the sides of ∠C with an arc. So, with the compass point on C, draw an arc intersecting the sides of ∠C (labeled A and B), which is option D. Option A is incorrect (compass on O too early), B is irrelevant (length CD not needed), and C is incorrect (intersecting the new construction too early).

After marking A and B on ∠C, we need to transfer that arc length to ∠D. Using the same compass setting (from AB) and placing the compass point on D (the vertex of the new angle), we draw an arc intersecting the ray from the first step (labeled R). This matches option C. Option A uses C (wrong vertex), B uses length AB but the logic of the step is about transferring the arc from ∠C, and D uses C (wrong vertex).

Answer:

B. Draw a ray and label the endpoint O.

Second Question (Second Step in the Construction)