讲解这道题---**Question 3** **Question Stem:** As shown in the figure, in the right triangular prism ABC-A₁B₁C₁, ∠BAC = 90°, AB = AC = 2. Points M and N are the midpoints of A₁C₁ and A₁B₁ respectively. **(1) Prove:** MN // plane BB₁C₁C; **(2) If:** CM ⊥ MN, find the volume of the triangular pyramid M-NAC. **Chart/Diagram Description:** * **Type:** Geometric figure, specifically a right triangular prism. * **Main Elements:** * The prism is named ABC-A₁B₁C₁, where ABC is the bottom base and A₁B₁C₁ is the top base. * **Vertices:** A, B, C, A₁, B₁, C₁. * **Edges:** * Solid lines: A₁B₁, B₁C₁, C₁A₁ (top base edges), BB₁, CC₁ (lateral edges), BC (bottom base edge), MN, CM, CN (internal connecting lines). * Dashed lines: AA₁, AB, AC (bottom base edges and lateral edge), AN, AM (internal connecting lines). * **Points:** * M is located on the edge A₁C₁. * N is located on the edge A₁B₁. * **Connectivity:** * Line segment MN connects point M and point N. * Line segment CM connects point C and point M. * Line segment CN connects point C and point N. * Line segment AN connects point A and point N. * Line segment AM connects point A and point M. * **Implied Geometry based on text:** * The base triangle ABC is a right-angled isosceles triangle with the right angle at A (∠BAC = 90°). * Sides AB and AC have length 2 (AB = AC = 2). * The prism is a "right" prism, meaning the lateral edges (AA₁, BB₁, CC₁) are perpendicular to the bases. * M is the midpoint of A₁C₁. * N is the midpoint of A₁B₁.

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