请解答用初中知识这一道题---Here is the extraction of the content from the image: **Question 20** **(1)** As shown in Figure ①, in square ABCD, points E and F are on sides CD and BC respectively. Connect AE, AF, ∠EAF = 45°. Explore the quantitative relationship between segments DE, BF, EF. Xiao Jun's thinking: Pass through point A, draw AG ⊥ AE intersecting the extension of CB at point G. It is easy to prove △ABG ≅ △ADE, thus getting ∠GAF = ∠EAF, AG = AE. Then it is easy to prove △AEF ≅ △AGF, which can solve the problem. According to Xiao Jun's thinking, complete the diagram in Figure ①. Please directly write the quantitative relationship between segments DE, BF, EF. **(2)** As shown in Figure ②, in square ABCD, points E and F are on the extensions of CD and BC respectively. Connect AE, AF, ∠EAF = 45°. Connect EF. Explore the quantitative relationship between segments DE, BF, EF, and explain the reason. **(3)** As shown in Figure ③, in rectangle ABCD, AB = 12, AD = 16. Points E and F are on rays DC and CB respectively. Connect AE, AF. Given ∠EAF = 45°, BF = 4, find the length of segment DE. **Figures** **图① (Figure 1)** * Type: Geometric figure. * Main Elements: * A square labeled ABCD. * Point E is on side CD. * Point F is on side BC. * Segments AE, AF, EF are drawn connecting the vertices and points. * Vertices labeled A, B, C, D in counter-clockwise order starting from the top left. **图② (Figure 2)** * Type: Geometric figure. * Main Elements: * A square labeled ABCD. * Point E is on the extension of side CD beyond D. * Point F is on the extension of side BC beyond C. * Segments AE, AF, EF are drawn. * Vertices labeled A, B, C, D. **图③ (Figure 3)** * Type: Geometric figure. * Main Elements: * A rectangle labeled ABCD. * Point E is on the ray DC (implies E could be on DC or its extension beyond C). From the diagram, E is on the extension of DC beyond C. * Point F is on the ray CB (implies F could be on CB or its extension beyond B). From the diagram, F is on the extension of CB beyond B. * Segments AE, AF are drawn. * Vertices labeled A, B, C, D. * A watermark "公众号★全科AB+" is present. **Other Relevant Text** * "第 20 题图" (Figure for Question 20) - Below the figures.