It is known that the upper middle points of AB and BC on both sides of triangle ABC are E.F. two points on AC are G.H. Ag = GH = HC,; Connect and extend EG.FH It is proved that ABCD is a parallelogram;

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• 1. Cut AE = BF = CG = DH on each side of square ABCD, connect AF, BG, CH and De, and intersect a ` B ` c ` d 'in turn. It is proved that quadrilateral a ` B ` c ` d' is a square
• 2. In the isosceles trapezoid ABCD, ab ∥ DC, ad = BC = 5, DC = 7, ab = 13, point P starts from point a and moves to the midpoint C along ad → DC at the speed of 2 unit lengths per second At the same time, point Q starts from point B and moves along Ba to terminal a at the speed of 1 unit length per second. Let the movement time be T seconds (1) When the value of T is, the quadrilateral pqbc is a parallelogram (2) In the whole movement process, when t is the value, the quadrilateral with points B, C, P and Q as the vertex is isosceles trapezoid
• 3. As shown in the figure, in rectangular ABCD, e is the point on BC and F is the point on CD. Given s △ Abe = s △ ADF = 13sabcd, then the value of s △ AEF: s △ CEF is equal to () A. 2B. 3C. 4D. 5
• 4. Let E and f be on the edge BC and CD of rectangular ABCD respectively, and the areas of △ Abe, △ ECF and △ FDA are a, B and C respectively. Find the area s of △ AEF
• 5. Rectangle ABCD, e and F are on BC and CD respectively. The area of triangle Abe, CEF and ADF are 2, 3 and 4 respectively
• 6. As shown in the figure, ABCD is a rectangle, e and F are the points on BC and CD respectively, and s △ Abe = 3, s △ CEF = 2, s △ ADF = 2, then s △ AEF = ()
• 7. As shown in the figure, in square ABCD, e and F are on BC and CD, respectively, ∠ EAF = 45 ° to prove s △ AEF = s △ Abe + s △ ADF
• 8. As shown in the figure, in square ABCD, e and F are on BC and CD, respectively, ∠ EAF = 45 ° to prove s △ AEF = s △ Abe + s △ ADF
• 9. In square ABCD, e and F are on BC and CD, respectively, ∠ EAF = 45 °, try to explain s △ AEF = s △ Abe + s △ ADF
• 10. It is known that the quadrilateral ABCD is a square with a side length of 6 cm. The area of the triangle ECF is 3 square cm larger than that of the triangle ADF
• 11. In △ ABC, E.F AB.CB G. h is fed to two points on AC, and Ag = GH = HC EG.FH Intersection at point D. proof: a quadrilateral ABCD is a parallelogram
• 12. As shown in the figure, in square ABCD, e and F are two points on BD, and be = DF
• 13. The quadrilateral ABCD is a diamond. The extension of de perpendicular to ab intersects BA at point E, and DF perpendicular to BC intersects BC at point F. please guess the size of De and DF
• 14. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
• 15. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
• 16. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
• 17. In the parallelogram ABCD, e and F are the points on the edge of AD and ab respectively, and be = DF, be and DF intersect at point G
• 18. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG
• 19. In the square ABCD, e is any point on the diagonal BD. if the circumference of the square ABCD is For m, find the perimeter of the quadrilateral EFCG
• 20. It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG