17.∠A=60，∠ABC= 120 .

18. As shown in the figure, the isosceles trapezoid ABCD, ad∨BC, diagonal AC⊥BD, AD=3, BC=7, DE⊥BC is in E, try to find the length of DE.

18. Hint: Find BD first, and from Rt△BDE ∠ DBE = 45, you can get DE=5.

19. As shown in the figure, in trapezoidal ABCD, AD∨BC, AM=MB, DN=NC.

Verification: (1)MN∨BC

(2)MN= (BC+AD)

19. Hint: Connect AN and extend it. The extension line of BC is at point E.

20. As shown in the figure, if it is known that in △ABC, D and E are the midpoint of AB and AC respectively, then DE∑BC and DE = BC can be obtained. According to the above conclusions:

(1) What special quadrilateral can be obtained by connecting the midpoints of any quadrilateral in sequence? And explain why.

(2) If "arbitrary quadrilateral" in (1) is changed to "parallelogram" or "rhombus" or "rectangle" or "isosceles trapezoid", what are their conclusions? Please provide a justification for the answer.

20.( 1) parallelogram; (2) parallelogram, rectangle, diamond and square.

Second, solve the problem:

17. As shown in the figure, after the rectangular ABCD paper is folded along EF, ed and BC intersect at G point, and D point and C point fall at D ′ and C ′ respectively.

If ∠ EFG = 55, find ∠AEG and ∠ECB degrees.

17.∠AEG=70，∠EGB= 1 10 .

18. As shown in the figure, in the known quadrilateral ABCD, AC=BD, and points E, F, G and H are the midpoints of AB, BC, CD and DA respectively.

It is proved that the quadrilateral EFGH is a diamond.

18. Hint: Prove by the midline theorem of triangle.

19. It is known that in the rectangular ABCD as shown in the figure, O is the diagonal intersection, OE⊥BC is in E, OE=2, and ∠ cab = 60, so find the rectangle.

The area of ABCD.

20. Point E is the point on the side BC of the square ABCD. Connect AE and find out what it is.

2 1. The picture shows some streets in a city. AF//BC, EC⊥BC, BA//DE, BD//AE, Party A and Party B take the bus from Mile Mile at the same time.

When the bus arrives at the next stop, A takes bus 1, and the route is B → A → E → F; B takes bus No.2, the route is B→D→C→F, assuming that the two cars have the same speed,

The delay time on the way is the same, so who will arrive at station F first, please explain the reason.

2 1. Two people arrive at the same time.

Just try it.