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### Câu 24:
You are asked to find the correct statement about the intersection \( AN \) of two planes \( (ACD) \) and \( (GAB) \), where \( G \) is the centroid of triangle \( BCD \) in the tetrahedron \( ABCD \).

We are given four options about the position of point \( N \):
- **A.** \( N \) is the midpoint of segment \( AB \).
- **B.** \( N \) is the midpoint of segment \( CD \).
- **C.** \( N \) is the midpoint of segment \( BD \).
- **D.** \( N \) is the midpoint of segment \( AC \).

From the geometry of the situation, we can deduce that since \( G \) is the centroid of triangle \( BCD \), and since the intersection of the two planes \( (ACD) \) and \( (GAB) \) gives the line \( AN \), **the correct option is A**, where point \( N \) is the midpoint of \( AB \).

### Câu 25:
You are tasked with identifying which statement about the midpoints \( M \), \( N \), \( P \), and \( Q \) of the edges of the tetrahedron \( ABCD \) is **false**.

The midpoints are as follows:
- \( M \) is the midpoint of \( AB \),
- \( N \) is the midpoint of \( AD \),
- \( P \) is the midpoint of \( CD \),
- \( Q \) is the midpoint of \( BC \).

We are given the following statements:
- **A.** \( MN \parallel BD \) and \( MN = \frac{1}{2} BD \).
- **B.** \( MN \parallel PQ \) and \( MN = PQ \).
- **C.** Quadrilateral \( MNPQ \) is a parallelogram.
- **D.** \( MN \) and \( PQ \) are not equal.

To analyze:
- **Statement A** is true, by the midpoint theorem, which tells us that \( MN \parallel BD \) and \( MN = \frac{1}{2} BD \).
- **Statement B** is also true, since \( MN \parallel PQ \) by the midline theorem, and their lengths are equal.
- **Statement C** is true as well, since opposite sides of quadrilateral \( MNPQ \) are parallel and equal in length, confirming that it forms a parallelogram.
- **Statement D** is false because it contradicts statement B, as \( MN \) and \( PQ \) are indeed equal.

Therefore, the **false statement is D**.

### Do you want further details or have any questions about these solutions? 

### Related Questions:
1. How do you determine the intersection of two planes in 3D geometry?
2. What is the significance of the centroid of a triangle in geometry?
3. How can you apply the midpoint theorem in 3D shapes?
4. Why do midpoints form a parallelogram in a tetrahedron?
5. How can you find the equation of a line formed by the intersection of two planes?

### Tip:
When working with 3D geometric figures like tetrahedrons, using spatial visualization or drawing projections can greatly help in understanding the relationships between points and planes.

Câu 24: Cho hình tứ diện ABCD. Gọi G là trọng tâm tam giác BCD. Giao tuyến của hai mặt phẳng (ACD) và (GAB) là AN với: A. Điểm N là trung điểm của AB. B. Điểm N là trung điểm của CD. C. Điểm N là trung điểm của BD. D. Điểm N là trung điểm của AC.
Câu 25: Cho tứ diện ABCD. Gọi M, N, P, Q lần lượt là trung điểm các cạnh AB, AD, CD, BC. Khẳng định nào sau đây SAI? A. MN \parallel BD và MN = \frac{1}{2} BD. B. MN \parallel PQ và MN = PQ. C. Tứ giác MNPQ là hình bình hành. D. MN không bằng PQ.

Solve geometry problems involving the tetrahedron ABCD, the centroid of triangle BCD, and midpoints of edges. Learn how to find the intersection of planes and apply the midpoint theorem. Suitable for students in Grades 10-12.

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