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

First, we prove that △ ade ≌ ABF, so ∠ AEA '= ∠ afb2. ∵ AE = BF, ∠ a'ae = ∠ Fab ≌ aa'e

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1. 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
2. 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
3. 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
4. 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
5. 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 = ()
6. 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
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. In square ABCD, e and F are on BC and CD, respectively, ∠ EAF = 45 °, try to explain s △ AEF = s △ Abe + s △ ADF
9. 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
10. As shown in the figure, it is known that the quadrilateral ABCD is a square with a side length of 5cm. The area of the triangle ECF is 5 square centimeters larger than that of the triangle ADF. Find the length of the line CE
11. 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;
12. 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
13. As shown in the figure, in square ABCD, e and F are two points on BD, and be = DF
14. 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
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. 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
19. 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
20. 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