这个题给我证明一下吧，用中文---1.如图，在三棱柱 ABC - A₁B₁C₁中，侧棱垂直于底面，AB⊥BC，AA₁=AC=2，BC=1，E，F 分别是 A₁C₁，BC 的中点. (1) 求证：AB⊥C₁F； (2) 求证：C₁F // 平面 ABE； (3) 求三棱锥 E - ABC 的体积. --- **Image Description:** * **Type:** Geometric figure illustrating a triangular prism ABC-A₁B₁C₁ with additional lines. * **Main Elements:** * **Vertices:** Labeled points A, B, C at the bottom base, and A₁, B₁, C₁ at the top base directly above A, B, C respectively. Points E and F are also labeled. * **Edges of the Prism:** Solid lines: AA₁, AC, CC₁, C₁B₁, C₁A₁, BC, AB. Dashed lines: AB₁, BB₁, AA₁, AC (partially dashed). All side edges (AA₁, BB₁, CC₁) are perpendicular to the base planes. * **Additional Lines:** Solid lines: C₁F, AE, BE, CE. Dashed line: A₁C₁, EF (implied by midpoints, though not explicitly drawn as a segment). * **Points E and F:** Point E is shown on the line segment A₁C₁. Point F is shown on the line segment BC. * **Relationships shown or implied by labels:** E is the midpoint of A₁C₁, F is the midpoint of BC. AB is perpendicular to BC (AB⊥BC). Side edges are perpendicular to the base (e.g., AA₁⊥plane ABC). * **Relative Position:** The prism is oriented such that the base ABC is at the bottom, and the top base A₁B₁C₁ is directly above it. Point F is on the edge BC. Point E is on the edge A₁C₁. Lines AE, BE, CE, and C₁F are drawn. Lines inside the figure that are hidden are shown as dashed lines.