Use the image to answer the question.

Question

Two line segments extend from point upper M. One slopes upward to the right. One slopes downward. The segments intersect the left side of a circle and terminate on the right side of the circle.

Thuy examines the figure in the image. She needs to determine if  NO¯¯¯¯¯¯¯¯
  is a copy of  PQ¯¯¯¯¯¯¯¯
 . What must she do to show that  NO¯¯¯¯¯¯¯¯
  is a constructed copy of  PQ¯¯¯¯¯¯¯¯
 ?

(1 point)

GPT-4o mini · Answer

To determine if line segment $ NO $ is a constructed copy of line segment $ PQ $, Thuy must show that the two segments are congruent. She can do this by following these steps: 1. **Measure the Lengths**: Thuy should measure the length of segment $ PQ $ and compare it to the length of segment $ NO $. If both segments are equal in length, this is the first indication that $ NO $ could be a copy of $ PQ $. 2. **Check the Properties**: Thuy can also check if both segments are placed at the same angle relative to the vertical or horizontal reference lines. This will help establish that they not only have the same length but are also oriented in a similar manner. 3. **Visualize or Overlay**: If possible, Thuy could use a transparent ruler or overlay to check if $ NO $ can be placed over $ PQ $ without any gaps or overlaps. 4. **Verify Endpoints**: If segments are constructed such that endpoints match correspondence and $ NO $ can be moved to lie exactly on top of $ PQ $, that will further support her claim. By completing these steps, Thuy can demonstrate that line segment $ NO $ is indeed a constructed copy of $ PQ $.