As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) prove: AC ‖ de; (2) make BF ⊥ AC at point F through point B, connect EF, try to distinguish the shape of quadrilateral BCEF, and explain the reason

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• 1. Quadrilateral ABCD, ad vertical BD, EF diagonal to o, ab = 6, ad = 4 of = 1.5, calculate the circumference of BCEF ABCD is a parallelogram. EF passes through the intersection o of diagonal line and intersects with AB and CD at points E and f respectively
• 2. If the side length of square ABCD is 1 and point P moves on line AC, then the maximum value of AP & nbsp; · (Pb + PD) is___ ．
• 3. In square ABCD, e is the midpoint of CD, P is ad, and angle APB = angle BPE. Then the value of Tan angle APB is
• 4. As shown in the figure, in square ABCD, take BC as the edge, make equilateral triangle BCE outside the square, connect De, then the degree of angle CFE is degree
• 5. As shown in the figure, point E is a point in the square ABCD, connecting AE, be and CE. Rotate △ Abe clockwise 90 ° around point B to the position of △ CBE '. If AE = 1, be = 2 and CE = 3, then ∠ be ′ C =... Degree
• 6. As shown in the figure, the quadrilateral ABCD is a square. Take AB as the edge, make an equilateral triangle Abe outside the square. The intersection of CE and BD and point F are used to calculate the degree of the angle AFD
• 7. As shown in the figure, in ladder ABCD, ad ‖ BC, ab = DC, ∠ ABC = 72 °, now move waist AB to de in parallel, and then fold △ DCE along De to get △ DC ′ e, then the degree of ∠ EDC ′ is______ Degree
• 8. As shown in the figure, in the quadrilateral ABCD, the point E is on BC, ∠ a + ∠ ade = 180 °, ∠ B = 78 ° and ∠ C = 60 ° to find the degree of ∠ EDC
• 9. As shown in the figure, in the parallelogram ABCD, ad ⊥ BD, ad = 4, do = 3 (1) find the perimeter of △ cod (2) find the parallelogram a
• 10. (1) which triangles are congruent in the graph? (2) Choose a pair of congruent triangles to prove
• 11. Parallelogram ABCD parallelogram abef is on the same side AB, m, n are on the diagonal AC, BF respectively, and am: AC = FN: FB to prove Mn / / plane ADF Try to be clear
• 12. As shown in the figure, ABCD and abef are two congruent squares that are not in the same plane. The points m and N are on the diagonal lines AC and BF respectively, and cm = BN. Prove: Mn / / plane BCE
• 13. It is known that ABCD and abef are two squares and not in the same plane, m and N are the points on the diagonal AC and FB respectively, and am = FN
• 14. It is known that, as shown in the figure, e and F are two points on the diagonal AC of the parallelogram ABCD, AE = CF
• 15. In ▱ ABCD, the bisector BC of ∠ bad is at point E, and the bisector DC is at point F (1) Prove CE = CF in Figure 1; (2) if ∠ ABC = 90 ° and G is the midpoint of EF (as shown in Figure 2), write the degree of ∠ BDG directly; (3) if ∠ ABC = 120 ° and FG ‖ CE, FG = CE, connect dB and DG respectively (as shown in Figure 3), and calculate the degree of ∠ BDG
• 16. It is known that in the parallelogram ABCD, points E and F are on AB and BC respectively. If △ ade, △ bef and △ CDF are 5, 3 and 4 respectively, what is the area of △ def
• 17. In square ABCD, M is the middle point of AB side, take a point E on ad to make AE = 1 / 4AD (1) Please judge the position relationship between me and MC and explain the reason. (2) if the area of this square is 64, find the length of EC (to use Pythagorean theorem)
• 18. As shown in the figure, in the quadrilateral ABCD, points E and F are on BC and CD respectively, and ab = AE = AF = ad = BC = CD = EF, then the degree of ∠ C
• 19. As shown in the figure, the quadrilateral ABCD is inscribed in ⊙ o, BC is the diameter of ⊙ o, e is a point on the side of DC, if AE ∥ BC, AE = EC = 7, ad = 6. (1) find the length of AB; (2) find the length of eg
• 20. As shown in the figure, the area ratio of triangle ABC to triangle ade is 3:4, and the area of triangle ABF is 10 square centimeter larger than that of triangle FCE