Question

naomi draws a portion of a figure, as shown. she wants to construct a line segment through r that makes the same angle with qr as pq. which figure shows the next step to construct a congruent angle at r?

Explanation:

Step1: Recall angle - construction steps

To construct a congruent angle, after drawing an arc from the vertex of the given angle (at Q in this case), we need to draw an arc with the same radius from the new vertex (R). Then, we measure the distance between the intersection points of the arc and the sides of the given angle (intersection points of the arc and PQ, QR) and transfer that distance to the new arc drawn from R.

Step2: Analyze the next - step figure

The next step should be to measure the distance between the intersection points of the arc and the sides of ∠PQR and use that distance to mark a point on the arc drawn from R. This is done by using a compass to transfer the length between the two intersection points on the arc at Q to the arc at R.

Answer:

The figure that shows an arc drawn from R with the same radius as the arc drawn from Q, and then a compass - setting to measure the distance between the intersection points of the arc and the sides of ∠PQR is the correct next - step figure. Without seeing the actual options clearly, the general correct next - step is to have an arc at R and a compass set to the length between the intersection points of the arc and the sides of the angle at Q. If we assume the options follow the standard construction steps, the figure where a compass is shown with the width set to the distance between the intersection points of the arc and the sides of ∠PQR and is about to mark a point on the arc at R is the answer.