Question

suppose we wish to construct, using compass and straightedge, angle dae congruent to angle dbc. which step would be correct to do first? a place the compass point at b. b place the compass point at c. c place the straightedge along a and c. d place the straightedge along c and d.

Explanation:

Step1: Recall the process of constructing congruent angles

To construct an angle congruent to a given angle (here, angle \(DBC\)) using compass and straight - edge, the first step is to work with the vertex of the given angle. The vertex of angle \(DBC\) is point \(B\).

Step2: Analyze each option

• Option A: Placing the compass point at \(B\) (the vertex of the given angle \(DBC\)) is the correct first step in the process of copying the angle. We can then use the compass to measure the "width" of the angle \(DBC\) (by drawing an arc that intersects both sides of the angle \(DBC\)).
• Option B: Placing the compass point at \(C\) (a non - vertex point of the given angle \(DBC\)) is not the first step. \(C\) is just a point on one of the sides of the angle \(DBC\).
• Option C: Placing the straightedge along \(A\) and \(C\) is not relevant to the initial steps of copying angle \(DBC\) to construct angle \(DAE\). \(A\) is the vertex of the angle we want to construct (\(DAE\)), and initially, we need to work with the given angle \(DBC\).
• Option D: Placing the straightedge along \(C\) and \(D\) is also not relevant to the first step of copying the angle \(DBC\). \(D\) is a point on the extension of the side of the angle we want to construct (\(DAE\))'s reference line, and \(C\) is a non - vertex point of the given angle \(DBC\).

Answer:

A. Place the compass point at B.