Let's analyze the problems from the image step by step:

Problem 7:

The transformation between the two triangles (one in Quadrant I and one in Quadrant III) is a rotation.

• Transformation: 180° rotation about the origin. When a figure is rotated 180° about the origin, the coordinates $(x, y)$ are transformed to $(-x, -y)$, which matches the change from the triangle in Quadrant I to Quadrant III.
• Congruence Statement: $\triangle ABC \cong \triangle XYZ$

Problem 8:

The two triangles appear to be identical in shape and orientation, but they are located on opposite sides of the $y$-axis. This suggests a reflection.

• Transformation: Reflection across the $y$-axis. The reflection of a point $(x, y)$ across the $y$-axis becomes $(-x, y)$, which aligns with the transformation seen here.
• Congruence Statement: $\triangle DEF \cong \triangle XYZ$

Problem 9:

In this problem, the two triangles are located on opposite sides of the $x$-axis. This indicates another reflection.

• Transformation: Reflection across the $x$-axis. The reflection of a point $(x, y)$ across the $x$-axis becomes $(x, -y)$, which matches the transformation here.
• Congruence Statement: $\triangle PQR \cong \triangle XYZ$

Problems 10-12:

For these problems, you need to list the congruent sides and angles for the triangles based on the given congruence statements.

• Problem 10: $\triangle JPM \cong \triangle TRW$

  • Congruent sides: $JP \cong TR$, $PM \cong RW$, and $JM \cong TW$
  • Congruent angles: $\angle J \cong \angle T$, $\angle P \cong \angle R$, and $\angle M \cong \angle W$

• Problem 11: $\triangle LUV \cong \triangle MTH$

  • Congruent sides: $LU \cong MT$, $UV \cong TH$, and $LV \cong MH$
  • Congruent angles: $\angle L \cong \angle M$, $\angle U \cong \angle T$, and $\angle V \cong \angle H$

• Problem 12: $\triangle CAT \cong \triangle SUP$

  • Congruent sides: $CA \cong SU$, $AT \cong UP$, and $CT \cong SP$
  • Congruent angles: $\angle C \cong \angle S$, $\angle A \cong \angle U$, and $\angle T \cong \angle P$

Would you like more details on any of these transformations or congruence statements?

Here are five related questions to expand your understanding:

1. How do you determine if two triangles are congruent using a transformation?
2. What are the key properties of a 180° rotation in the coordinate plane?
3. Can any triangle be reflected across the origin and still be congruent to its preimage?
4. What are the different types of rigid transformations that preserve triangle congruence?
5. How do you use the coordinates of vertices to confirm a reflection or rotation?

Tip: To check if a transformation preserves congruence, remember that translations, rotations, and reflections are all isometries, meaning they preserve distances and angles.