解---**Extraction Content:** **Question Stem:** 20. 如圖 (十一), △ABC 中, D 點在 BC 上, 且 BD 的中垂線與 AB 相交於 E 點, CD 的中垂線與 AC 相交於 F 點。已知 △ABC 的三個內角皆不相等, 根據圖 (十一) 中標示的角, 判斷下列敘述何者正確？ **Options:** (A) ∠1 = ∠3, ∠2 = ∠4 (B) ∠1 = ∠3, ∠2 ≠ ∠4 (C) ∠1 ≠ ∠3, ∠2 = ∠4 (D) ∠1 ≠ ∠3, ∠2 ≠ ∠4 **Other Relevant Text:** 圖 (十一) **Chart/Diagram Description:** * **Type:** Geometric figure, specifically a triangle with internal points and lines. * **Main Elements:** * **Points:** Vertices of the triangle are labeled A, B, C. Point D is on the side BC. Point E is on the side AB. Point F is on the side AC. * **Lines/Segments:** The triangle ABC is formed by segments AB, BC, and AC. Segment AD connects A to D. A vertical line segment passes through E and appears to be perpendicular to BC (or potentially related to the perpendicular bisector of BD). A vertical line segment passes through F and appears to be perpendicular to BC (or potentially related to the perpendicular bisector of CD). Lines connect A to E, E to D, A to F, and F to D. * **Angles:** Four angles are labeled numerically: * ∠1 is formed by segments AE and ED. * ∠2 is formed by segments ED and DB. * ∠3 is formed by segments AF and FD. * ∠4 is formed by segments FD and DC. * **Relative Position and Direction:** Points B, D, C are collinear, forming the base BC. E is on AB, F is on AC. The vertical line through E intersects BC at some point (implied to be the midpoint of BD by the text description). The vertical line through F intersects BC at some point (implied to be the midpoint of CD by the text description). The diagram visually represents these perpendicular lines intersecting BC. E is connected to D, F is connected to D, and A is connected to D. * **Labels and Annotations:** Points are labeled A, B, C, D, E, F. Angles are labeled 1, 2, 3, 4. The diagram is labeled "圖 (十一)". * **Perpendicular Bisectors:** The text states that the perpendicular bisector of BD intersects AB at E, and the perpendicular bisector of CD intersects AC at F. The diagram visually shows vertical lines through E and F meeting BC, suggesting they are related to perpendicular lines, but doesn't explicitly show them as perpendicular bisectors or indicate midpoints of BD and CD on BC. However, based on the text, the line through E perpendicular to BC at the midpoint of BD should contain E, and similarly for F and CD. The diagram shows vertical lines passing through E and F and intersecting BC, consistent with this description if BC is assumed horizontal.