Question

c) the construction of copying is started below. the next step is to set the width of the compass to the length of. how does this step ensure that the new angle will be congruent to the original angle?

Explanation:

Step1: Recall compass - angle - construction principle

In angle - copying construction, setting the compass width based on the intersection points of the arc with the original angle's rays creates congruent segments.

Step2: Use SSS (Side - Side - Side) congruence

When we set the compass width from the intersection points on the original angle's rays and replicate it for the new angle, we are creating three pairs of congruent sides (the two radii of the arcs and the segment between the intersection points of the arc with the rays). By SSS congruence criterion, the new angle will be congruent to the original angle.

Answer:

Setting the compass width to the length between the intersection points of the arc with the original angle's rays ensures congruence of the new angle to the original angle by the SSS congruence criterion.