此解题思路以及使用的知识点---**Extraction Content:** **(Question Worth 9 Points)** As shown in the figure, in △ABC, ∠ACB is an acute angle, point D is a moving point on ray BC, connect AD, construct an isosceles right triangle ADF above AD with AD as a leg, such that ∠ADF=90°, AD=DF, connect CF, BD. (1) As shown in Figure 1, when point D is on line segment BC, investigate the quantitative relationship and positional relationship between CF and BD. (2) When point D is on the extension of line segment BC, is the conclusion in ① still valid? Please draw the corresponding figure in Figure 2 and provide explanation. (3) As shown in Figure 3, if AB=AC, ∠BAC≠90°, point D moves on ray BC, ∠BCA=45°, investigate the positional relationship between CF and BD. **Chart/Diagram Description:** There are three geometric figures labeled 图1, 图2, and 图3. **图1 (Figure 1):** - Type: Geometric figure. - Main Elements: - Triangle ABC. - Point D is located on the line segment BC. - Line segments AD, CF, and BD are drawn. - An isosceles right triangle ADF is constructed such that AD and DF are sides of the right angle at D (∠ADF = 90°), and AD = DF. Triangle ADF is positioned "above" AD relative to triangle ABC. - Labels: A, B, C, D, F. **图2 (Figure 2):** - Type: Geometric figure. - Main Elements: - Triangle ABC. - Point D is located on the extension of line segment BC, beyond C. - Line segments AD, CF, and BD are drawn. - An isosceles right triangle ADF is constructed such that AD and DF are sides of the right angle at D (∠ADF = 90°), and AD = DF. Triangle ADF is positioned "above" AD relative to triangle ABC. - Labels: A, B, C, D, F. **图3 (Figure 3):** - Type: Geometric figure. - Main Elements: - Triangle ABC, where AB and AC are stated to be equal (isosceles triangle). - Point D is located on the line segment BC. - Angle BCA is labeled as 45°. - Line segments AD, CF, and BD are drawn. - An isosceles right triangle ADF is constructed such that AD and DF are sides of the right angle at D (∠ADF = 90°), and AD = DF. Triangle ADF is positioned "above" AD relative to triangle ABC. - There is a symbol indicating a right angle at point D on the line segment BC, suggesting that AD is perpendicular to BC in this specific illustration, although D is described as a moving point on the ray BC in the text. - Labels: A, B, C, D, F.