Proving that two geometric shapes are the same size and shape can be tricky. Here are some challenges you might face:

1. Transformations: This is how we change the shape. The main ways are:

   • Translation: Sliding the shape.
   • Rotation: Turning the shape.
   • Reflection: Flipping the shape.

   Figuring out the right way to combine these can be hard and take a lot of work.

2. Identification: It's not always easy to see or calculate which parts of the shapes match up. This can make it confusing to tell if the shapes really are the same after the changes.

3. Verification: After making the changes, we need to check if the sides and angles of the shapes are the same. This can feel like a lot of work.

Even with these challenges, we can make things easier:

• Step-by-step Approach: Take it slow. Work on one transformation at a time instead of trying to do everything all at once.

• Use Coordinates: Draw the shapes using coordinates. This can make math easier.

• Utilize Technology: Software tools can help us see the changes and check if the shapes are the same, making everything less scary.

By tackling these challenges one by one, we can prove that geometric shapes are congruent, meaning they are the same!