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The image contains several questions about cubes and their geometric properties. I'll work through each question, providing answers and explanations.

1. **Cube \( ABCD.EFGH \) with side length 10 cm:**
   - **(a) Two pairs of parallel lines:**
     - \( AB \parallel EF \)
     - \( AD \parallel EH \)
   - **(b) Two pairs of skew lines:**
     - \( AB \) and \( EG \)
     - \( AD \) and \( FG \)
   - **(c) Two pairs of lines perpendicular to each other:**
     - \( AB \perp AD \)
     - \( EF \perp EH \)

2. **Cube \( PQRS.TUVW \) with side length 18 cm and point \( A \) at the midpoint of line \( QV \):**
   - **(a) Distance from point \( K \) to point \( A \):**
     - Assuming \( K \) is a vertex, and using the cube's geometry, the distance can be calculated based on the diagonal properties of the cube.
   - **(b) Distance from point \( Q \) to line \( TV \):**
     - This involves calculating the perpendicular distance between a point and a line in 3D space, using the coordinates of \( Q \) and \( TV \).
   - **(c) Distance from point \( R \) to plane \( PAS \):**
     - This would involve determining the perpendicular distance from point \( R \) to the plane formed by points \( P, A, S \).

3. **Cube \( ABCD.EFGH \) with side length 20 cm. If \( Q \) is the midpoint of line \( GH \), find the distance from point \( E \) to line \( HQ \):**
   - This problem requires calculating the distance from point \( E \) to the line using vector methods or geometry, as the point \( Q \) divides the line \( GH \) into equal parts.

4. **Cube \( ABCD.EFGH \) with side length 10 cm. Find the distance from point \( F \) to line \( AC \):**
   - This is another 3D distance calculation between a point and a line in the cube.

5. **Cube \( ABCD.EFGH \) with side length 12 cm. If point \( M \) is the intersection point of diagonals \( AC \) and \( BD \), find the distance from point \( M \) to line \( AH \):**
   - The intersection point \( M \) is the center of the cube. The distance from the center to an edge can be found using geometric properties of the cube, specifically by calculating distances between midpoints and edges.

Would you like detailed calculations for any of these questions? Let me know if you'd like further explanations!

### Related Questions:
1. How do you calculate the distance between two skew lines in 3D?
2. What is the formula for finding the distance from a point to a plane in 3D geometry?
3. How do you determine the intersection point of two diagonals in a cube?
4. How can you find the angle between two lines in 3D space?
5. What is the geometric meaning of the centroid in 3D shapes like cubes?

### Tip:
When working with 3D geometry, visualizing the figure or drawing a sketch can greatly help in understanding the spatial relationships between points, lines, and planes.

Diketahui beberapa soal mengenai kubus dan sifat geometrinya. Setiap soal memerlukan perhitungan jarak antara titik, garis, dan bidang pada kubus dengan panjang rusuk yang berbeda.

This page covers detailed solutions for geometry problems involving 3D cubes, focusing on calculating distances between points, lines, and planes within cubes of various sizes. Learn key concepts like perpendicularity, parallelism, and using vector methods.

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