As shown in the figure, ab = AE, BC = ed. ∠ B = ∠ E. f is the midpoint of CD. Explain the reason why AF ⊥ CD .A one 1 1 1 1 1 1 1 1 1 1 1 1 B 1 1 1 E 1 1 1 1 1 1 one hundred and eleven million one hundred and eleven thousand one hundred and eleven C F D

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• 1. As shown in the figure, ab = AE, angle B = angle e, BC = ed, f is the midpoint of CD, and verify that AF is vertical to CD
• 2. As shown in the figure, in the regular pentagon ABCDE, ab = AE, BC = ed, angle B = angle e, and point F is the midpoint of CD
• 3. As shown in the figure, in the Pentagon ABCDE, BC = De, AE = DC, angle c = angle e, DM is perpendicular to AB and M is the midpoint of ab
• 4. As shown in the figure, in the pentagonal ABCDE, ∠ BAE = 120 °, ∠ B = ∠ e = 90 °. AB = BC, AE = De, find a point m, N on BC, de respectively, so that the perimeter of △ amn is the smallest, then the degree of ∠ amn + ∠ anm is () why extend AB to a 'to make Ba' = AB, extend AE to a 'to make AE = EA' ', connect a'm, a'n, then the perimeter of △ amn is the smallest?
• 5. As shown in the figure, in the pentagonal ABCDE, ∠ BAE = 120 °, ∠ B = ∠ e = 90 °, ab = BC, AE = De, find a point m and N on BC and de respectively to minimize the perimeter of △ amn, then what is the degree of ∠ amn + ∠ anm
• 6. It is known that ab = AE, BC = ed, AF is the vertical bisector of CD, as shown in the figure
• 7. As shown in the figure, ab = AE, BC = ed, ∠ B = ∠ e, AF ⊥ CD, foot drop is f, which means that AF bisects CD
• 8. In the Pentagon ABCDE, if angle a = angle c = 90 degrees, ab = BC = de = AE + CD = 3, what is the area of the Pentagon?
• 9. As shown in the figure, in the Pentagon ABCDE, BC = 4, CD = 4-ab, AE = de = 6, AE ⊥ AB, de ⊥ CD______ ．
• 10. As shown in the figure: ab = AE, BC = ed ∠ B = ∠ E. verify that ∠ C = ∠ D is a Pentagon, and the counter clockwise letter is ABCDE
• 11. As shown in the figure, the angle B = ∠ C = 90 °, M is a point on BC, and DM bisects ∠ ADC, am bisects ∠ DAB, proving: ad = CD + ab
• 12. In trapezoidal ABCD, ad is parallel to BC, triangle ADC is 2:3 than triangle ABC, and the connecting line of diagonal midpoint m and N is 10 cm Finish it today as soon as possible
• 13. In trapezoid ABCD, ab ‖ CD, ∠ ABC = 90 °, ab = 5, BC = 10, Tan ∠ ADC = 2. (1) find the length of DC; (2) e is a point inside the trapezoid, f is a point outside the trapezoid, if BF = De, ∠ FBC = ∠ CDE, try to judge the shape of △ ECF, and explain the reason. (3) under the condition of (2), if be ⊥ EC, be: EC = 4:3, find the length of de
• 14. In a trapezoid ABCD, AB is parallel to CD, angle BCD equals 90 degrees, AB equals 1, BC equals 2, Tan angle ADC equals 2, and E is a point in the trapezoid The angle EDC is equal to the angle FBC and De is equal to BF. Try to judge the shape of triangle ECF and prove your conclusion
• 15. In the trapezoid ABCD, AB / / DC, CE are bisectors of angle BCD, and CE is perpendicular to ad, de = 2ae. CE divides the trapezoid into two parts: S1 and S2. If S1 = 1, s is obtained Sorry, there's no picture S1 is a quadrilateral abce, S2 is a triangle ECD
• 16. As shown in the figure, in ladder ABCD, ad ‖ BC, be bisects ∠ ABC, and be ⊥ CD is the first moving point on be. If BC = 6, CE = 2DE, then the maximum value of | pc-pa | is______ ．
• 17. Known: as shown in the figure, in quadrilateral ABCD, angle DAB = 60 degrees, angle B = angle, ADC = 90 degrees, CD = 2, BC = 11, find the length of AC
• 18. In the trapezoid ABCD, ab | CD, the perimeter is 27, de | BC intersects AB at point E, CD = 4, what is the perimeter of the triangle ade
• 19. If the circumference of trapezoid ABCD is 25cm, ab \ \ CD, de \ \ BC and intersects AB with E, what is the circumference of triangle ade Can you give me more details? Maybe there are other ways?
• 20. As shown in the figure, in the quadrilateral ABCD, ∠ bad = ∠ BCD = 90 ° AB = ad, if the area of the quadrilateral ABCD is 24cm2, then the AC length is______ cm．