As shown in the figure, in square ABCD, e is a point on CD, f is a point on BC extension line, CE = cf. (1) prove: △ BCE ≌ △ DCF; (2) if ∠ BEC = 60 °, calculate the degree of ∠ EFD

(1) It is proved that: ∵ ABCD is a square, ∵ DC = BC, ∵ DCB = ∵ FCE, ∵ CE = CF, ∵ DCF ≌ △ BCE; (2) ∵ BCE ≌ △ DCF, ∵ DFC = ∵ BEC = 60 °,

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1. E is on CD, f is a point on the extension line of BC, CE = CF (1) proves that triangle BCE congruent triangle DCF (2) ∠ FD E is on CD, f is a point on BC extension line, CE = CF (1) Proof of triangle BCE congruent triangle DCF (2) How much is ∠ FDC = 30 ° and ∠ bef = 0
2. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference
3. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference
4. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference
5. As shown in the figure, in the isosceles trapezoid ABCD, ad = 4cm, BC = 8cm, e is the midpoint of the waist AB, CE divides the trapezoid circumference into two parts, the difference is 3cm, and calculates the trapezoid circumference
6. In the trapezoidal ABCD, ab = 8, ad = 5, CD = 6, BC = 15. Point E is on the bottom BC, and point F is on the waist CD. EF bisects the area and perimeter of ABCD at the same time to find the length of CE
7. In the isosceles trapezoid ABCD, AD / / BC, assuming BC = 4, ad = 8, angle a = 45 degrees, the area of the trapezoid is calculated
8. As shown in the figure, in the trapezoidal ABCD, ad ‖ BC, ∠ B = 90 °, ab = 14cm, ad = 18cm, BC = 21cm, point P starts from point a, moves at 1cm / s along side ad to point D, and point Q starts from point C, moves at 9cm / s along side CB to point B. If one point moves to the end point, the other point stops. If P and Q start at the same time, can a quadrilateral PQCD become an isosceles trapezoid? If so, how many seconds? If not, please give reasons
9. As shown in the figure, in the trapezoidal ABCD, ad ‖ BC, ∠ B = 90 °, ab = 4cm, ad = 18cm, BC = 21cm, point P starts from point a, moves 2cm / s along edge ad to point D, point Q starts from point C, moves 6cm / s along edge CB to point B, P and Q start at the same time, if one point moves to the end point, the other point stops=______ Cm; 2______ Second, PQ = CD
10. Let AB = a, ad = B, BC = 2B (a > b). Make de ⊥ DC, de intersect AB at point E, connect EC. (1) try to judge whether △ DCE and △ ade, △ DCE and △ BCE are similar. (2) for the above judgment, if the two triangles must be similar, please prove it. (3) if not, please point out when a and B satisfy what relationship, they can be similar?
11. As shown in the figure, in square ABCD, e is a point on the edge of CD, f is a point on the extension line of BC, CE = CF
12. As shown in the figure, in the square ABCD, f is a point on CD, AE ⊥ AF, point E is on the extension line of CB, EF intersects AB at point G, proving: de · FC = BG · EC
13. As shown in the figure, the point E is on the diagonal BD of the square ABCD, and be = AB, EF ⊥ BD, EF and CD intersect at the point F to prove de = EF = FC
14. As shown in the figure, in square ABCD, e is a point on the edge of BD, and be = BC, EF is perpendicular to BD, intersecting CD with F
15. As shown in the figure, take a point E on the diagonal BD of square ABCD, make be = BC, make ef vertical BD, intersect CD with F. the line segment De is equal to EF and FC? Why?
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