Question

question 8 (essay worth 2 points) (mc) the figure shows a construction made using technology. does the construction demonstrate how to copy an angle correctly using technology? explain why or why not by describing how it was constructed.

Explanation:

To copy an angle using technology (or traditional compass - and - straightedge), we first draw a ray. Then, with the vertex of the original angle as the center, we draw an arc that intersects the two sides of the original angle at two points. We then use the same radius on the new ray with its endpoint as the center to draw an arc. Next, we measure the distance between the two intersection points on the original arc and transfer that distance to the new arc. If these steps are correctly followed in the given construction, the angle is copied correctly. In the given figure, we need to check if the following steps are present: 1. An arc is drawn from the vertex of the original angle ($\angle B$) intersecting its sides at $F$ and $G$. 2. An arc of the same radius is drawn from the vertex of the new ray ($A$) intersecting the ray at $H$. 3. The distance between $F$ and $G$ is transferred to the new arc to get point $I$. If all these steps are done accurately, the construction is correct. From the figure, it appears that the construction follows the steps of copying an angle. An arc is drawn from $B$ intersecting the sides of $\angle B$, an arc of the same radius is drawn from $A$, and it seems that the distance between the intersection points on the arc of $\angle B$ is used to find point $I$ on the arc from $A$. So, the construction demonstrates how to copy an angle correctly.

Answer:

Yes, the construction demonstrates how to copy an angle correctly. The steps of drawing an arc from the vertex of the original angle, drawing an arc of the same radius from the vertex of the new ray, and transferring the distance between the intersection - points on the original arc to the new arc seem to be followed.