The correct figure (Chart 4) shows the next step to construct a line segment through R, creating the desired congruent angle. This figure ensures that the angle at R is the same as the angle at Q, maintaining the congruency with line segment PQ.
To construct a line segment through R that makes the same angle with line segment QR as line segment PQ, we can follow these steps:
1. Begin by drawing a compass arc from point Q as shown in the first chart.
2. Place the compass at point P and draw another arc that intersects the previous arc. Label the point of intersection as R.
3. Now, we need to construct a line segment through R that makes the same angle with line segment QR as line segment PQ.
4. Look at each of the given figures (Charts 2, 3, 4, and 5) to determine the correct next step.
5. Examine Chart 2: This figure does not construct a line segment through R. It does not provide the desired congruent angle.
6. Examine Chart 3: This figure also does not construct a line segment through R. It is not the correct next step.
7. Examine Chart 4: This figure constructs a line segment through R, creating the desired congruent angle. It is the correct next step.
8. Examine Chart 5: This figure constructs a line segment through R, but it does not create the desired congruent angle.
So, Chart 4 is the correct figure that shows the next step to construct a line segment through R, making the same angle with line segment QR as line segment PQ.
The diagram cannot be made as charts are not provided in the question