讲解一下这道题---**Question 27** **Textual Information:** Known, as shown in the figure, in △ABC, ∠ACB=90°, ∠ABC=45°. Point D is on the extension of BC, point E is on the extension of CB. DC=BE. Connect AE. Draw CF perpendicular to AE at F. CF intersects AB at G. Connect DG. (1) Prove: ∠AEB=∠ACF; (2) Express the quantitative relationship between CG, DG, and AE using an equation, and prove it. **Chart/Diagram Description:** * **Type:** Geometric figure illustrating a set of points, lines, and triangles. * **Main Elements:** * **Points:** Labeled points are A, B, C, D, E, F, G. * **Lines:** * A straight line segment passes through points D, C, B, E in that order. * A vertical line segment AC is perpendicular to the line segment DE at point C. A right angle symbol is shown at C. * Line segments AB, BC, and CA form triangle ABC. * Line segment AE connects A and E. * Line segment CF is drawn from C, intersecting AE at F. A right angle symbol is shown at F, indicating that CF is perpendicular to AE. * Line segment CF intersects line segment AB at G. * Line segment DG connects D and G. * Line segment CG connects C and G. * **Shapes:** * Triangle ABC is a right-angled triangle at C. * Several other triangles are formed by the intersections of lines, including △ADE, △ACE, △DGC, △CFB, △CGE, △AFG, △BGE. * **Angles:** * ∠ACB is explicitly marked as a right angle (90°). * ∠CFE (or ∠CFA) is explicitly marked as a right angle (90°) due to CF ⊥ AE. * Given ∠ABC=45°. * **Labels and Annotations:** All key points (vertices, intersections) are labeled with capital letters (A, B, C, D, E, F, G). Right angle symbols are present at vertices C and F. * **Relative Position and Direction:** * Points D, C, B, E are collinear on a horizontal line. C is to the left of B. D is to the left of C. B is to the left of E. * Point A is positioned above point C. * Point F is on the line segment AE. * Point G is the intersection of line segments CF and AB. * Line segment CF passes through G.