1. (Yichang, Hubei) As shown in the figure, BC = 6, and E and F are line segments respectively.

The midpoint between AB and AC segment, the length of EF segment is ().

6 (B)5 (C)4.5 (D)3

2 (Suzhou, 2005) As shown in the figure, the center line of the isosceles trapezoid ABCD is known.

If the length of EF is 6 and the length of waist AD is 5, then the circumference of isosceles trapezoid is ().

a . 1 1 b . 16 c . 17d . 22

3. (Hebei, 2004) As shown in the figure, in the trapezoid, ABCD, AD//BC, diagonal AC⊥BD, and AC= 12, BD=9, then the midline length of this trapezoid is ().

A.B.

C.D.

4. (Yuxi City, 2005) As shown in the figure, EF is called the center line of trapezoidal ABCD.

If ab = 8, BC = 6 and CD = 2, then the bisector of ∠B intersects EF and G,

The length of FG is ()

A. 1 B. 1.5 C.2 D.2.5

5. (Taizhou, 2005) As shown in the figure, ABCD, AD//BC and BD in the trapezoid are diagonal lines.

The neutral line EF intersects BD at point O. If fo-EO = 3, BC-AD is equal to ().

A.4 B.6 C.8 D. 10

6. As shown in the figure, in trapezoidal ABCD, AD‖BC, E and F are the midpoint of AB and DC, respectively, and EF intersects BD and G, AC and H. If AD=2, BC=5, GH = _ _ _ _ _ _ _ _ _

7. (Guangzhou) As shown in the figure, ABCD, AO⊥BD, OE, FG, HL in the box.

Perpendicular to AD, EF GH IJ perpendicular to AO,

If S△AIJ= 1 is known, then the square of s ABCD=.

8. (Hu 05) In △ABC, point D and point E are on AB side and AC side respectively.

And DE‖BC, if AD=2, DB=4, AE=3, then EC=.

9. (Heilongjiang 05) At the same time, the height of the object is directly proportional to the length of the shadow. Xiao Ming's height is 1.5 meters, and his shadow length on the ground is 2 meters. At the same time, the shadow length of an ancient pagoda on the ground is 40 meters, so the height of the ancient pagoda is ().

A.60 B.40 C.30 D.25

10. (Xiamen 2005) As shown in the figure, in △ABC, ∠ ade = ∠ c, then the following equation holds ().

A.ADAB = AEAC·AEBC = ADBD

C.DEBC=AEAB D. DEBC=ADAB

1 1. (Lianyungang, 2005) If each side of a triangle is expanded to five times the original size, then each angle of the triangle ().

(a) They have all been expanded fivefold; (b) They are all expanded to 65,438+00 times.

(c) Both of them have been expanded to 25 times; (d) Both are equal to the original.

12. (Haidian 05) As shown in the figure, in the trapezoidal ABCD, AB‖DC, ∠ B = 90.

E is a little above BC, AE⊥ED. If BC= 12, DC=7,

BE:EC= 1:2, find the length of AB.

13. In the plane rectangular coordinate system, points A (-3,0), B (0 0,4) and C (0, 1) are known as straight lines passing through point C and intersecting with point D, so that a triangle with points D, C and O as vertices is similar to △AOB, and such a straight line can be * *.

A. One article B. Two articles C. Four articles D. Eight articles

14. As shown in the figure, the length AD = 9CM, the width AB = 4cm, the AE = 2cm, and the line segment MN = 3 cm. Both ends of the line segment MN slide on CB and CD. When ⊿ADE is similar to a triangle with m, n and c as vertices, the length of cm is cm. 15 (.

Then there are () (A) 1 pair (B)2 pairs (C)3 pairs (D)4 pairs of similar triangles.

16. pinhole imaging problem) according to the size in the picture on the right.

(‖) Then the image is long (long)

An image that is a function of the length of an object.

Roughly ()

17. (Beijing, 2005) As shown in the figure, in the parallelogram ABCD, E is a point on AD, connecting CE, and extending the extension line of intersection BA to point F, then the following conclusion is wrong ().

A.∠AEF =∠DEC b . FA:CD = AE:BC c . FA:AB = FE:EC d . AB = DC

18. (Changde, 2005) As shown in the figure, de is the center line of δδABC.

The area ratio of δδADE to δδABC is () a.1:1B.1:2c.1:3d.1:4.

19. (Longyan, 2004) Cut a triangular iron sheet with a circumference of 20 cm into four pieces with complete shapes and sizes.

The same small triangular iron sheet (as shown in the figure), the circumference of each small triangular iron sheet

The length is centimeters.

20. As shown in the figure, AO is the bisector of △ABC ∠A, BD⊥AO,

The extension line of AO is at d, and e is the midpoint of BC. Proof: DE= (AB-AC).

2 1. As shown in the figure, E and F put the diagonal BD of quadrilateral ABCD.

The extension lines of CE and CF are divided into AB and AD respectively.

It is proved that the quadrilateral ABCD is a parallelogram.

22. Verification: The line connecting the diagonal midpoint of the quadrilateral and the line connecting the midpoint of the opposite side are equally divided.

23. As shown in the figure, in the quadrilateral ABCD, AB=CD, and E and F are the midpoint of AD and BC respectively.

BA and FE are extended to G and CD and FE to H. Verification: ∠ 1=∠2.

24. As shown in the figure, trapezoidal ABCD, AB‖DC, AB+CD=8, AB:CD=7:3.

E and f are the midpoint of AC and BD, respectively. Find the length of EF.

25. As shown in the figure, in △ABC, P is the midpoint of AB and D is the midpoint of AP.

E, q is the midpoint of AC, CD, f is the midpoint of PQ, EF passes through AB to g,

Verification: DG=BG.

26. (Guangdong Province in 2005) As shown in the figure, in the isosceles trapezoid, ABCD, AD‖BC, M and N are respectively.

Is the midpoint of AD and BC, and e and f are the midpoint of BM and CM respectively.

(1) Verification: quadrilateral MENF is a diamond;

(2) If the quadrilateral MENF is a square, please explore the isosceles trapezoid ABCD.

The relationship between height and bottom BC, and prove your conclusion.

27. (Ziyang, Sichuan) As shown in Figure 5, the known points M and N are the sides BC of △ABC respectively.

The midpoint of AC, point P is the symmetrical point of point A about point M, and point Q is the symmetrical point of point B about point N,

Prove that P, C and Q are on the same straight line.

28. As shown in the figure, in quadrilateral ABCD, AC=6, BD=8, and AC⊥BD sequentially connects the midpoints of each side of quadrilateral ABCD to obtain quadrilateral A1b1c1d1; Then connect the midpoints of the sides of the quadrilateral A1B1C1D1in turn to get the quadrilateral A2B2C2D2…… .....................................................................................................

(1) It is proved that quadrilateral A1b1c1d1is a rectangle;

(2) Write the area of quadrilateral A1b1c1d1and quadrilateral A2B2C2D2;

(3) Write the area of quadrilateral AnBnCnDn;

(4) Find the perimeter of the quadrilateral A5B5C5D5.

29. as shown in the figure, AD bisects ∠BAC, DE‖CA, AB= 15,

AC= 12, find the length of DE.

30. it is known that d is on the BC side of △ABC, DF‖BA,

DE‖CA，DE∶DF= 1∶2，AB=6，AC=4，

Find the length of DE.

3 1. Known: As shown in the figure, in △ABC, AD bisects ∠BAC, AB=5,

AC=3, BC=5.6, find the length of BD and DC.

32. It is known: As shown in the figure, ABCD and E are points on the extension line of CD and BE.

Cross AD to F, AB= 12, DE=3, BE=30, and find the length of BF and EF.

33. It is known that ABCD and E are the midpoint of BC, BF= AB, EF and.

Diagonal BD intersects G, if BD=20, find the length of BG.

34. As shown in the figure, in △ABC, the straight line DE intersects with AB, AC and BC at D, E,

f，AE=BF

Verification:

35. As shown in the figure, AD is the center line of△ △ABC, and E is the upper point of AD.

The CE extension line passes through AB to f,

Verification:

36. As shown in the figure, AD is the center line of△ △ABC, and M is the midpoint of AD.

The BM extension line passes through AC to n,

Verification: AN∶CN= 1∶2

37. As shown in the figure, m and n are the midpoint of AB and CD, respectively.

AD and BC pass through MN to e and f respectively.

Verification: ED∶EA=FC∶FB

38. As shown in the figure, AD⊥BC is in D, and E is the midpoint of AC, connecting DE and BA in F.

Verification:

39. As shown in the figure, ABCD, AC and BD are given to O, and O OF is given to BC and E,

Cross the AB extension line to f,

Proof: BE(AB+2BF)=BC? novio

40. As shown in the figure, D and E are points on the sides of AB and AC respectively, which connect d E and extend the extension line of intersection BC to F, and AD=AE.

Verification:

4 1. (6 points in this question) As shown in the figure, in the right triangle ABC, ∠ c = 90, AC = 8°, BC = 6°, AB2=AC2+BC2 will AB.

Divided into ten parts, P 1, P2, ..., P9 are all equal integrals, even CP 1, CP2, ..., CP9. Please find a pair of similar triangles in the figure.

And explain why they are similar.

42. (Wuxi, 2005) It is known that the side length of each small square in Figure 1 and Figure 2 is 1 unit.

(1) Translate the grid point △ABC in the figure 1 by 3 units to the right, and then by 2 units to get △A 1B 1C 1. Please draw △ a 1 b65438 in the drawing1.

(2) Draw a lattice triangle similar to the lattice △DEF in Figure 2, but the similarity ratio is not equal to 1.

43. As shown in the figure, in △ABC, ∠ C = 90, AC = 6°, BC = 8°, m is the midpoint of BC, P is a moving point on AB (which can coincide with A and B), and ∠ MPD = 90, and PD intersects BC (or the extension of BC) at point D.

(1) Remember that the length of BP is X, and the area of △BPM is Y. Find the functional relationship between Y and X, and write the range of independent variable X;

(2) Is there such a point p that △MPD is similar to △ABC? If it exists, request the value of x; If it does not exist, please explain why.