请出一个本试题的解析视频---**Overall Title:**
A佳查分经典易错题—每周一题 (新初三)
**Subtitle:**
A佳经典易错题 (10亿+大数据统计)
**Table:**
| 试题来源 | 满分 | 平均得分 | 得分率 |
| :------------- | :--- | :------- | :------ |
| 新中考模拟试卷 | 10 | 3.21 | 32.15% |
**Question Stem (Question 25):**
25、(10分) 如图1, 在Rt△ABC中, ∠A=30°, AB=6, 点D在AB上, 且AD=2BD. 点E是AC上一个动点, 从点A向点C移动, 连接DE, 以DE为直角边, 向DE右侧作Rt△DEF, 且满足∠EDF=90°, ∠DFE=30°, 连接CF, 记∠ADE=α.
**Sub-questions:**
(1) 连接CD, 求线段CD的长;
(2) 如图1, 当0° < α < 30°时, DF交AC于点G, 求证: CF⊥AC;
(3) 如图2, 当α = 60°时, 求证: 四边形DECF是矩形;
(4) 如图3, 当30° < α < 90°时, 判断CF与AC的位置关系, 并说明理由.
**Chart/Diagram Descriptions:**
**Diagram 1 (图1):**
* **Type:** Geometric figure, illustrating a dynamic geometry setup involving triangles and line segments.
* **Main Elements:**
* **Points:** Labeled points A, B, C, D, E, F, G.
* **Shapes:**
* A right-angled triangle ABC (Rt△ABC) with angle ∠A = 30°. The problem statement "Rt△ABC" implies the right angle is at C (∠C=90°).
* Point D is located on the side AB. A right angle symbol at D indicates that the line segment CD is perpendicular to AB (CD ⊥ AB).
* Point E is a moving point on the side AC.
* Line segment DE connects points D and E.
* A right-angled triangle DEF (Rt△DEF) is constructed on the right side of DE. A right angle symbol at D indicates ∠EDF = 90°.
* Line segment DF forms part of △DEF, with ∠DFE = 30°.
* Line segment CF connects points C and F.
* Point G is the intersection of line segment DF and line segment AC.
* **Angles:** ∠A = 30°. ∠ADE is denoted as α. ∠EDF = 90°. ∠DFE = 30°.
* **Lines:** Line segments AB, BC, AC, CD, DE, EF, DF, CF are shown.
* **Labels:** The diagram is labeled "图1".
**Diagram 2 (图2):**
* **Type:** Geometric figure, a specific configuration of the setup described for Diagram 1, illustrating the case when α = 60°.
* **Main Elements:**
* All points (A, B, C, D, E, F) and constructions (Rt△ABC, CD ⊥ AB, Rt△DEF) are consistent with Diagram 1.
* The arrangement of points and segments visually suggests that the quadrilateral DECF might be a rectangle under this specific condition (α = 60°), which is the property to be proven in sub-question (3).
* Right angle symbols are shown at D (for CD ⊥ AB and ∠EDF=90°).
* **Labels:** The diagram is labeled "图2".
**Diagram 3 (图3):**
* **Type:** Geometric figure, another specific configuration of the setup described for Diagram 1, illustrating the case when 30° < α < 90°.
* **Main Elements:**
* All points (A, B, C, D, E, F) and constructions (Rt△ABC, CD ⊥ AB, Rt△DEF) are consistent with Diagram 1 and Diagram 2.
* The arrangement of points and segments visually represents the situation for the specified range of angle α in sub-question (4).
* Right angle symbols are shown at D (for CD ⊥ AB and ∠EDF=90°).
* **Labels:** The diagram is labeled "图3".
**Footer:**
可私信老师领取答案解析 (日期: 2025.7.30)