Math Problem Statement

Cho hình chóp S.MNPQ có đáy MNPQ là hình vuông. Gọi E, F lần lượt là trung điểm của SM, SN. a) Chứng minh rằng: EF // MN. Từ đó suy ra EF // (MNPQ). b) Chứng minh rằng: EF // (SPQ). c) Tìm giao tuyến của hai mặt phẳng (SMP) và (SNQ). d) Tìm giao tuyến của hai mặt phẳng (SMQ) và (ENP).

Solution

This image appears to be a geometry problem in Vietnamese related to a rectangular prism (hình chóp vuông) with various geometric tasks to prove. Let me help you analyze the tasks:

  1. Task (a): Prove that EFMNEF \parallel MN. From the statement, it's implied that EE and FF are midpoints of SMSM and SNSN, respectively, so proving this will involve using properties of midpoints in parallel lines or using vectors.

  2. Task (b): Prove that EFSPQEF \parallel SPQ. This requires showing that line EFEF is parallel to the plane formed by SPQSPQ, using geometrical reasoning based on perpendicularity or projections.

  3. Task (c): Find the intersection of two planes: SMPSMP and SNQSNQ. This requires finding the line formed where these two planes intersect.

  4. Task (d): Find the intersection of planes SMQSMQ and ENPENP. Similar to part (c), this involves identifying the line of intersection between these two planes.

Would you like help with the detailed proof or analysis of these tasks, or is there a specific part you'd like to focus on?

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel lines
Planes of intersection
Midpoints

Formulas

Properties of parallel lines
Intersection of planes formula

Theorems

Midpoint Theorem
Parallelism of lines in space

Suitable Grade Level

Grades 10-12