The image contains several geometry problems related to three-dimensional shapes, such as prisms, cubes, and pyramids. Let's solve each of these problems step-by-step:

Problem 1:

It mentions angles formed by certain line segments within a triangular prism $ABC.DEF$. We need to identify which line segments create angles with each other. This involves determining the geometric properties of the given prism.

Problem 2:

The problem involves a cube $ABCD.EFGH$ and asks for the angles formed between different lines and planes in the cube. Understanding the relationships between lines within the cube will allow us to find the angles.

Problem 3:

This problem focuses on a regular triangular pyramid (tetrahedron) $TABC$. It asks for the angles formed between the planes, which requires knowledge of dihedral angles in tetrahedrons.

Problem 4:

The problem involves identifying angles between various edges and diagonals in another cube $ABCD.EFGH$. Determining these angles requires an understanding of 3D geometry principles.

Problem 5:

It discusses identifying angles between certain lines in a square-based pyramid $T.ABCD$.

Each problem involves calculating or identifying angles between different line segments or planes in three-dimensional shapes.

Would you like me to solve each problem one-by-one or provide detailed explanations for any specific problem? Let me know how you'd like to proceed!

Further Questions for Exploration:

1. What are the different types of angles formed in a cube, and how do you calculate them?
2. How can dihedral angles be calculated in a regular tetrahedron?
3. What are the properties of line segments and planes in a regular square pyramid?
4. How are angles between skew lines calculated in three-dimensional geometry?
5. What methods can be used to visualize three-dimensional geometric problems more effectively?

Tip:

Understanding 3D geometry requires a good grasp of spatial visualization. Try drawing the shapes and labeling all key points, lines, and planes to better understand their relationships.