The image explains how to construct congruent segments and congruent angles using a compass and a straightedge. Here is a summary of the instructions:

Steps to Construct a Congruent Segment

1. Step 1:

   • Begin with a given segment and label its endpoints $A$ and $B$.
   • Set the compass to the radius $AB$.

2. Step 2:

   • Draw a point $C$ not on the segment.
   • Sweep an arc from point $C$ using the compass setting from Step 1.
   • Any point on the arc can serve as the other endpoint of the congruent segment.

Steps to Construct a Congruent Angle

1. Step 1:

   • Draw an angle $\angle TSP$ and name it.

2. Step 2:

   • Draw a ray $\overrightarrow{GH}$. This ray will be one side of the congruent angle.

3. Step 3:

   • Use a compass to draw an arc centered at $S$ that intersects both sides of $\angle TSP$ (at points $T$ and $P$).

4. Step 4:

   • Label the points of intersection $A$ and $B$ for further construction.

Key Visuals:

• First diagram: Construction of a congruent segment using arcs centered at point $C$.
• Second diagram: Steps to construct a congruent angle, focusing on drawing arcs from the vertex $S$ and replicating the angle structure using ray $\overrightarrow{GH}$.

Relative Questions:

1. How can you verify that two segments are congruent using only a compass?
2. What is the significance of arcs in constructing congruent angles?
3. How can you replicate an angle if no straightedge is available?
4. What is the role of labeling intersection points in geometric construction?
5. How can you construct perpendicular bisectors using a compass and straightedge?

Tip: When working with a compass, ensure that the radius remains consistent to avoid construction errors.

Do you need further explanations or examples for these steps? 😊