When a rectangular piece of paper ABCD is folded along EF, the intersection points of ED and BC are g, D and C at M and N, respectively. If ∠ EFG = 55 °, then ∠ 1=______ °，∠2=______ °．

When a rectangular piece of paper ABCD is folded along EF, the intersection points of ED and BC are g, D and C at M and N, respectively. If ∠ EFG = 55 °, then ∠ 1=______ °，∠2=______ °．

∵ ad ∥ BC, ∠ EFG = 55 °, ∠ def = ∠ FEG = 55 °, ∠ 1 + ∠ 2 = 180 ° can be obtained from the properties of folding, ∠ GEF = ∠ def = 55 °, ∠ 1 = 180 ° - ∠ GEF - ∠ def = 180 ° - 55 ° - 55 ° = 70 ° and ∠ 2 = 180 ° - 1 = 110 °

As shown in the figure, the width of rectangular paper ABCD is ab = 3, folded along EF, and the intersection of ED edge and BC edge is at point O. if ∠ AEH = 60 °, the length of crease EF is______ ．

Let FG ⊥ ad be set at point G, then in the right angle △ EFG, FG = AB = 3, ∠ GEF = 12 (180 ° - ∠ AEH) = 12 (180 ° - 60 °) = 60 ° and 〈 sin ⊥ GEF = fgef = 3ef = sin60 ° = 32, the solution is EF = 2

When a rectangular piece of paper ABCD is folded along EF, the intersection points of ED and BC are g, D and C at M and N, respectively. If ∠ EFG = 55 °, then ∠ 1=______ °，∠2=______ °．

∵ ad ∥ BC, ∠ EFG = 55 °, ∠ def = ∠ FEG = 55 °, ∠ 1 + ∠ 2 = 180 ° can be obtained from the properties of folding, ∠ GEF = ∠ def = 55 °, ∠ 1 = 180 ° - ∠ GEF - ∠ def = 180 ° - 55 ° - 55 ° = 70 ° and ∠ 2 = 180 ° - 1 = 110 °

As shown in the figure, fold a rectangular piece of paper ABCD with side lengths of 4 and 8 so that point C coincides with point a, then the length of crease EF is ()
A. 3B. 23C. 5D. 25

According to the properties of folding, the quadrilateral afeb is congruent with the quadrilateral cefd, which has EC = AF = AE. According to the Pythagorean theorem, AB2 + be2 = AE2, that is, 42 + (8-ae) 2 = AE2, the solution is AE = AF = 5, be = 3, eg ⊥ AF at point G, then the quadrilateral ageb is rectangular, Ag = 3, GF = 2, Ge = AB = 4, and EF = 25 is obtained from the Pythagorean theorem