制作此题动态讲解视频---**Problem Header:** 22. (12分) **Given Conditions:** 已知□ABCD, AD⊥BD, DA=DB, 在直线BD上有一个动点E, 连接AE, AE=m. (Given parallelogram ABCD, AD is perpendicular to BD, DA equals DB, there is a moving point E on line BD, connect AE, AE equals m.) **Part (1):** **Condition for (1):** 如图1, 当点E在线段BD上时, ∠AED=75°. (As shown in Figure 1, when point E is on line segment BD, angle AED is 75 degrees.) **Sub-question (1)①:** 填空: ∠BAE=_________°; (Fill in the blank: angle BAE equals _________ degrees;) **Sub-question (1)②:** 若CD = 2√3+2, 求m的值; (If CD = 2√3+2, find the value of m;) **Handwritten Notes for Part (1):** ① ∠DAE=90-75=15, ∠BAE=45-15=30. ② ③x+x=2√3+2, x=2, m=2x=4. **Part (2):** **Condition for (2):** 若点E在线段DB上, 直线AE交直线CD于点F, 过点B作直线AE的垂线交AE于点G, 直线BG交直线CD于点H, 连接HE, 若HE=n, 求HB的值 (用含有m、n的式子表示); (If point E is on line segment DB, line AE intersects line CD at point F, draw a perpendicular line from point B to line AE intersecting AE at point G, line BG intersects line CD at point H, connect HE, if HE=n, find the value of HB (expressed using m and n);) **Part (3):** **Condition for (3):** 若AD=3, 以点A为旋转中心, 将线段AE逆时针旋转60°得到线段AE', 作直线BE', 当直线BE'与直线AC相交所成的锐角为60°时, 请直接写出BE'的值. (If AD=3, with point A as the center of rotation, rotate line segment AE counterclockwise by 60° to get line segment AE', draw line BE', when the acute angle formed by line BE' and line AC is 60°, please directly write out the value of BE'.) **Diagram Descriptions:** **图 1 (Figure 1):** * **Type:** Geometric figure (Parallelogram with internal lines). * **Main Elements:** * **Points:** A, B, C, D (vertices of a parallelogram ABCD), E (on line segment BD), F (on AB, though not explicitly labeled in the question, seems implied by handwritten x), G (not shown in this diagram). * **Lines:** AB, BC, CD, DA (sides of the parallelogram). BD (diagonal). AD is perpendicular to BD (indicated by a right angle symbol at D). AE (line segment, labeled m). BE (line segment, labeled x). * **Shapes:** Parallelogram ABCD, right triangle ABD. * **Angles:** Right angle at D formed by AD and BD. * **Labels:** AE is labeled m. BE is labeled x. Handwritten labels: 'x' near BE, '√3x' near AE (within triangle ABE), 'x' on a perpendicular from E to AB. There's also a label '30°' handwritten near angle BAE. * **Relative Position:** E is on the line segment BD. **备用图 (Spare Diagram - Middle):** * **Type:** Geometric figure (Parallelogram with internal and external lines). * **Main Elements:** * **Points:** A, B, C, D (vertices of a parallelogram ABCD). E (on line BD). F (on line CD, extension of AE). G (on AE). H (on line CD, intersection of BG and CD). T (on line CD extension). * **Lines:** AB, BC, CD, DA (sides of the parallelogram). BD (diagonal). AE (line segment). AE extended to F on CD. BG (line segment, perpendicular to AE at G). BG extended to H on CD. HE (line segment). * **Angles:** A right angle symbol is present where BG intersects AE at G. * **Labels:** E is labeled, H is labeled, F is labeled, G is labeled, T is labeled. AE is labeled m. HE is labeled n. * **Relative Position:** E is on BD. F is on the line CD. G is on AE. H is on the line CD. T is on the extension of CD. BG is perpendicular to AE. **备用图 (Spare Diagram - Right):** * **Type:** Geometric figure (Parallelogram). * **Main Elements:** * **Points:** A, B, C, D (vertices of a parallelogram ABCD). * **Lines:** AB, BC, CD, DA (sides of the parallelogram). BD (diagonal). AC (implied diagonal, though not drawn). * **Shapes:** Parallelogram ABCD. * **Labels:** Points A, B, C, D are labeled. **Other Handwritten Notes (partially visible, below diagrams):** > FH = EH - n (Partial text, context unclear) > Other scribbles and symbols (e.g., arrows, brackets, calculations that are mostly cut off).