As shown in the figure, the quadrilateral ABCD is a rectangle, ad = 3, ab = 4. Fold the rectangle along the line AC, point B falls at point E, and connect De, then the length of De is () A. 1B. 95C. 725D. 75

Let d be DF ⊥ AC in F, let e be eh ⊥ AC in H. as shown in the figure, ∵ quadrilateral ABCD is a rectangle, ∵ RT △ ABC ≌ RT ≌ CDA, and ∵ rectangle is folded along the straight line AC, so that point B falls at point E, ∵ RT ≌ ABC ≌ RT ≌ AEC, ≌ ADC ≌ CEA, ≌ CE = ad. according to the equal areas of congruent triangles, DF = eh

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1. Quadrilateral ABCD is a rectangle, ab = 4cm, ad = 3cm, fold the rectangle along the straight line AC, and point B falls at e to connect de. what is the figure of quadrilateral aced? What's its area? What's its perimeter?
2. As shown in the figure, the quadrilateral ABCD is a rectangle, AB: ad = 4:3, fold the rectangle along the straight line AC, point B falls at point E, and connect De, then de: AC = 1___ ．
3. In rectangle ABCD, ab = 10cm, ad = 3cm, fold the rectangle along the straight line AC, point B falls at point E, connect De, what is the figure of quadrilateral aced, and explain the reason And calculate its area
4. As shown in the figure, the quadrilateral ABCD is a rectangle, ab = 4AD = 3, fold the rectangle along the straight line AC, point B falls at point E, connect De, what is the figure of quadrilateral aced What about perimeter and area
5. Rectangle ABCD is discounted along diagonal, ab = 4, ad = 3, what is quadrilateral aced Area is also required
6. As shown in the figure, fold the rectangular piece of paper ABCD, first fold out the crease BD, and then fold so that the ad side coincides with the diagonal BD, and get the crease dg. if AB = 2, BC = 1, then the length of Ag is___ ．
7. As shown in the figure, in rectangular paper ABCD, ab = 4, ad = 3, fold the paper so that the ad side coincides with the diagonal BD, and the crease is DG, then the length of Ag is () A. 1B. 43C. 32D. 2
8. As shown in the figure, fold the rectangular piece of paper ABCD, first fold the crease (diagonal) BD, and then fold so that the ad edge coincides with BD, and get the crease DG, if AB = 4, BC = 3, find the length of Ag
9. As shown in the figure, fold the rectangular piece of paper ABCD, first fold out the crease BD, and then fold so that the ad side coincides with the diagonal BD, and get the crease dg. if AB = 2, BC = 1, then the length of Ag is___ ．
10. As shown in the figure, in rectangular ABCD, fold △ ABC along AC to △ AEC position, CE and ad intersect at point F. (1) try to explain: AF = FC; (2) if AB = 3, BC = 4, find the length of AF
11. As shown in the figure, e and F are the points on the diagonal AC and BD of rectangular ABCD, and AE = DF
12. As shown in the figure, fold the rectangular piece of paper ABCD along the diagonal AC, so that point B falls at point E. verify: EF = DF
13. In rectangle ABCD, ab = 10, BC = 8, fold the rectangle along AC, point d falls at point E, and CE and ab intersect at point F, then the length of AF is
14. In rectangle ABCD, ab = 4, BC = 6, fold the rectangle along AC, point d falls at e, and CE and ab intersect with F, then AF length is AB is not = 4, it is = 8
15. As shown in the figure, in rectangle ABCD, ab = 16, BC = 8, fold the rectangle along AC, point d falls at point E, CE and ab intersect at point F, (1) prove: AF = CF (2) find the length of AF
16. As shown in the figure, in rectangle ABCD, ab = 16, BC = 8, fold the rectangle along AC, point d falls at point E, and CE and ab intersect at F, then AF=______ ．
17. It is known that in square ABCD, ∠ man = 45 ° and ∠ man rotates clockwise around point a, and its two sides intersect CB and DC (or their extension lines) at points m and N respectively. When ∠ man rotates around point a to BM = DN (as shown in Figure 1), it is easy to prove that BM + DN = Mn (1) When ∠ man rotates around point a to BM ≠ DN (as shown in Figure 2), what is the quantitative relationship among BM, DN and Mn? Write out the conjecture and prove it; (2) when ∠ man rotates around point a to the position as shown in Fig. 3, what is the quantitative relationship among line segments BM, DN and Mn? Please write your guess directly
18. In square ABCD, am intersects BC at m, an intersects DC at n. angle man is 45 degrees. Angle man rotates clockwise around a, and its two sides intersect CB and DC at m respectively In square ABCD, am intersects BC at point m, an intersects DC at point n. angle man is 45 degrees. Angle man rotates clockwise around point a, and its two sides intersect CB and DC at point m and N respectively. When angle man rotates around point a to BM = DN, it is easy to prove BM + DN = Mn. When angle man rotates around point a to BM not = DN, what is the relationship between them?
19. As shown in the figure, in the square ABCD with side length of 8, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB with G, intersect CD with H. if cm = 2, then GH=______ ．
20. As shown in the figure, square ABCD, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB at point G, intersect CD at point h. given am = 10cm, find the length of GH