1. If △ ABC △DEF, the circumference of △ def is 32cm, DE=9cm, EF= 13cm. ∠E=∠B, then AC = _ _ _ _ _ _

2. As shown in the figure, someone broke a triangular piece of glass into three pieces. Now you want to go to a glass shop to match an identical piece of glass. Which piece of glass should you take to _ _ _ _ _ _ _ (fill in the glass serial number).

3. Given that ∠ BAC = 60 in △ABC, rotate △ABC clockwise by 40, as shown in the figure, the degree of △BAC' is _ _ _ _ _ _.

4. As shown in the figure, points D, E, F and B are on the same straight line, AB‖CD, AE‖CF, AE = CF If BD= 10, BF=2, EF = _ _ _ _ _ _ _ _

5. In △ABC, AC=4 and median AD=6, then the value range of AB side is _ _ _ _ _ _ _ _.

6. As shown in the figure, CD⊥AB, BE⊥AC, vertical feet are D, E, BE and CD intersect at point O, ∠ 1=∠2, in which congruent triangles * * * has _ _ _ _ pairs.

7. As shown in the figure, in △ABC, ∠ c = 90, AD divides ∠BAC, BC= 10cm, BD=6cm, then the distance from point D to AB is _ _ _ _ _ _ _.

8. As shown in the figure ∠ E = ∠ F = 90, ∠B=∠C, AE=AF, and the following conclusions are given: ① ∠1= ∠ 2; ②BE = CF； ③△ACN?△ABM； ④CD=DN. The correct conclusion is _ _ _ _ _ (fill in serial number).

9. As shown in the figure, it is known that Station A on the railway is 45km away from bilibili (regarded as two points on the line), C and D are two villages on the same side of the railway (regarded as two points), DA⊥AB is in A, CB⊥AB is in B, DA=25km, and CB=20km. Now, it is necessary to build a purchasing station E on the railway AB, so that C and D can.

10, as shown in the figure, at △ABC, ∠ C = 90, AC=BC, and AD share ∠CAB.

If BD is in D, DE⊥AB is in E, and AB= 10, then the circumference of △DEB is _ _ _ _ _.

Second, multiple-choice questions (3 points × 10=30 points)

1 1, as shown in figure △ ABC △ bad, points A and B, and points C and D are corresponding points.

If AB=6cm, BD = 5 cm and AD = 4 cm, then the length of BC is ().

A, 4cm B, 5cm C, 6cm D, uncertain.

12, as shown in figure △ Abe △ ACD, AB=AC, BE=CD, ∠ B = 50,

∠ ∠DAC = 120, then ∠∠ the number of DACs is equal to ()

a、 120 B、70 C、60 D、50

13, in △ABC and △ A ′ B ′ C ′, it is known that ∠ A = ∠ A ′, AB = A ′ B ′,

The error in the following judgment is ()

A, if conditions AC=A'C', △ ABC △ a' b' c' are added.

B, if BC=B'C', then △ ABC △ a' b' c'

C, if the addition condition ∠B=∠B', then △ ABC △ a' b' c'

D, if the addition condition ∠C=∠C', then △ ABC △ a' b' c'

14. Workers and masters often use a square to divide any angle. As shown in the figure, OM = on the sides OA and OB of ∠AOB respectively, move the square to make the same scales on both sides of the square coincide with M and N respectively, and get the bisector OP of ∠AOB. In practice, the judgment method of triangle congruence is ().

a、SSS B、SAS C、ASA D、HL

15, the following proposition is wrong ()

A, the line segments corresponding to congruent triangles are equal; Congruent triangles is the same size.

C, an acute angle and an adjacent right-angled side correspond to the coincidence of two right-angled triangles.

D, two angles correspond to the congruence of two triangles.

16, the condition that two triangles cannot be judged to be congruent is ()

A, trilateral equality; B, two sides and their included angles are equal.

C, two corners and one side are equal; D, the angles corresponding to two sides and one side are equal.

17, in △ABC and △ A ′ B ′ C ′, ① AB = A ′ B ′; ②BC = B′C′； ③AC = A′C′； ④∠A =∠A′； ⑤∠B =∠B′； ⑥∠C=∠C', which of the following conditions cannot guarantee △ ABC△ a ′ b ′ c ′ ()?

a、①②③ B、①②⑤ C、①⑤⑥ D、①②④

18, as shown in figure △ABC, ∠ C = 90, AB=2BC, D = AB, D = DE⊥AB, AC = E, and the following conclusions are drawn: ②AE = BC； ③∠B = 2∠A； ④ The correct number in ∠ a = 30 is ().

a， 1 b，2 c，3 d，4

19, as shown in the figure, in △ABC, AB=AC, BF=CD, BD=CE, ∠FDE=α, then the following conclusion is correct ().

A、2 α+∠A= 180 B、α +∠A=90

c、2α+∞A = 90d、α+∞A = 180

20. As shown in the figure, it is known that in △ABC, AQ=PQ, PR=PS, PR⊥AB is in R, and RS⊥AC is in S, so there are three conclusions: ① As = AR; ②QP AR； ③△BRP?△QSP()

A, all correct B, only ① and ② are correct.

C, only ① is correct, and only ① and ③ are correct.

Third, answer questions.

2 1, called △ def △ MNP, and EF=NP, ∠F=∠P, ∠ D = 58, ∠ E = 62, MN= 10cm, find ∠. (5 points)

22. As shown in the figure, D is a point on AB, DF meets AC at E, AE=CE, FC‖AB, and verification: DE=EF. (5 points)

23. As shown in the figure, △ABC is an equilateral triangle, with points M and N on BC and AC respectively, BM=CN, AM and BN intersecting at point Q, and the number of times to find ∠AQN. (6 points

24. As shown in the figure, point E is outsiDE △ABC, point D is on BC side, and de intersects with AC at point F. If ∠ 1=∠2 =∠3, AC=AE, verification: AB=AD. (6 points)

25. As shown in the figure, in a square ABCD, e is the midpoint of AD, f is a point on the extension line of BA, and AF= AB. What is the relationship between the line segment BE and the size and position of DF? And prove your conclusion. (7 points)

26. As shown in the figure, AB‖CD, BE bisects ∠ABC, and point E is the midpoint of AD, and BC=AB+CD. Prove that CE bisects ∠BCD. (7 points)

27. As shown in the figure, it is known that in △ABC, AB=AC, ∠ BAC = 90, and the straight lines passing through B and C respectively are vertical lines, and the vertical feet are E and F respectively.

(1) As shown in the figure, ① If the straight line passing through A does not intersect with the oblique side BC, it is verified that EF=BE+CF(4 points).

(2) As shown in the figure, when the straight line passing through A intersects with the hypotenuse BC, other conditions remain unchanged. If BE= 10 and CF=3, try to find the length of FE. (4 points)

28. In the rectangular coordinate system xOy, the straight line AB with O as the coordinate origin is parallel to the straight line: y = x, intersecting with the X axis at point A (-3,0), intersecting with the Y axis at point B, points M and N on the X axis (point M is on the left of point N), point N is MP⊥BN on the right of the origin, and the vertical foot is P (point P is on the line segment BN).

(1) Find the analytical formula of straight line AB and the coordinates of point B; (4 points)

(2) Find the coordinates of point m; (4 points)

(3) Let ON=t and the area of △MOG be S, find the functional relationship between S and T, and write the range of independent variable T; (4 points)

(4) If A is an acute vertex, and the right triangle ADF of the right vertex D on the X axis is the same as the right triangles of vertices A, O and B, let F(a, b) and find the values of A and B (only write the results, not the solution process). (4 points

The following proposition is correct ()

A. congruent triangles is of equal height. The median lines of congruent triangles are equal.

C the angular bisectors of congruent triangles are equal. D the bisectors of the corresponding angles in congruent triangles are equal.

2. The following conditions, can't make a unique triangle is ().

A, knowing two sides and included angle B, knowing two angles and clamping side.

C. Diagonal angle of two known edges and one of them

4. In the following groups of conditions, it is () that can determine △ ABC △ def.

A.AB=DE，BC=EF，∠A=∠D

B.∠A=∠D，∠C=∠F，AC=EF

C.AB=DE, BC=EF, and the perimeter of △ABC = the perimeter of △ def.

D.∠A=∠D，∠B=∠E，∠C=∠F

5. As shown in the figure, in △ABC, ∠A:∠B:∠C=3:5: 10, while △ MNC △ ABC,

Then ∠ BCM: ∠ BCN equals ()

1:2 b . 1:3 c . 2:3d . 1:4

6. As shown in figure ∠AOB and a fixed-length line segment A, find a point P in ∠AOB to make P.

The distance to OA and OB is equal to A, as follows: (1) as the vertical line NH of OB,

Let NH=A and h be vertical feet. (2) Let n be nm∨OB. (3) Let nature take its course ∠AOB.

The branch line OP that intersects with NM at point P. (4) is the demand.

The basis of (3) is ()

A. the distance between parallel lines is equal everywhere.

B the points with equal distance to both sides of the corner are on the bisector of the corner.

The point on the bisector of an angle is equal to the distance on both sides of the angle.

D, the points with the same distance to the two ends of the line segment are on the middle vertical line of the line segment.

7. As shown in the figure, the lengths of AB, BC and CA on the three sides of △ABC are 20, 30 and 40 respectively, and three of them are

If the angular bisector divides △ABC into three triangles, then S △ ABO: S △ BCO: S △ Cao is equal to ().

a . 1︰ 1︰ 1 b . 1︰2︰3 c . 2︰3︰4d . 3︰4︰5

8. As shown in the figure, from the following four conditions: ① BC = b' c, ② AC = a' c,

③ ∠ A ′ CB = ∠ B ′ CB, ④ AB = A ′ B ′, take one of the conditions,

The remaining one is a conclusion, so the number that can constitute the correct conclusion at most is ().

1。

9. To measure the distance between two opposite points A and B on both sides of the river, first on the vertical line BF of AB.

Take two points, C and D, so that CD=BC, and then determine the vertical line DE of BF, so that A, C and E are in the same place.

On a straight line, as shown in the figure, you can get it, so ED=AB, because

The measurED length of ed is the length of AB, and the reason for judgment is ()

A.B. C. D。

10. As shown in the figure, △ABE and △ADC are △ABC along the edges of AB and AC respectively.

If ∠ 1: ∠ 2: ∠ 3 = 28: 5: 3, then ∠ α times.

The number is ()

A.80 B. 100 C.60 D.45

Second, fill in carefully and record your confidence!

1 1. As shown in the figure, in △ABC, AD=DE, AB=BE, ∠ A = 80,

Then ∠ ced = _ _ _ _.

12. Given that △DEF △ABC, AB=AC, and the circumference of △ ABC is 23cm, BC=4 cm, then one of the sides of △ def must be equal to _ _ _ _ _.

13. In △ABC, ∠ c = 90, BC=4CM, in D, ∠ the bisector of ∠BAC intersects BC, and BD \u DC = 5 \u 3, then the distance from D to AB is _ _ _ _ _ _ _ _ _.

14. As shown in the figure, △ABC is an equilateral triangle, and DE=BC. With D and E as two vertices, make triangles in different positions, so that the triangle is congruent with △ABC, and at most _ _ _ such triangles can be drawn.

15. As shown in the figure, it is the height of the acute triangle and the middle edge of the acute triangle respectively. If it is, please supplement the condition _ _ _ _ _ _ _ _ _. (Just fill in one condition you think is appropriate)

17. If the height of two sides of two triangles and one of them is equal, then the relationship between the angles of the third sides of the two triangles is _ _ _ _ _ _ _.

19. As shown on the right, it is known to be in the middle and flat.

Points, in, if, then.

The circumference of is.

20. In the math activity class, Xiao Ming asked such a question: ∠B=∠C=90, and E is.

The midpoint of BC, DE bisects ∠ADC, ∠CED=35, as shown in the figure, what is ∠EAB?

Degree? We had a heated discussion and exchange, and Xiaoying got the correct answer first, which was _ _ _ _ _.

Third, do it calmly and show your wisdom!

2 1. As shown in the figure, there is a winding road in the park, among which

∨ Every place has a small stone bench.

For the midpoint, are the three small stone benches in a straight line?

State the reasons for your inference.

22. As shown in the figure, five equivalence relations are given: ① ② ③ ④.

Please take two of them as the conditions and one of the other three as the conclusion to derive a correct one.

Conclusion (write only one case) and prove it.

Known:

Verification:

Prove:

23. As shown in the figure, take ∠OA, OA on both sides of OB, OM=ON on OB, OD=OE respectively.

DN and EM intersect at point C.

Verification: Point C is on the bisector of ∠AOB.

Fourth, divergent thinking, handy!

24.( 1) As shown in figure 1, squares and squares are made with edges and edges outward respectively.

Link, try to judge the relationship with the region, and explain the reasons.

(2) The paths in the garden are winding and secluded, as shown in Figure 2, with white square marble and black triangular marble paths.

It is known that the sum of the areas of all squares in the middle is the sum of the areas of all triangles in the inner circle.

It's square meters. How many square meters is this path?

Reference answer

I.1-5: dcdcd6-10: bcbba

Second, 1 1. 100.

12.4cm or 9.5cm.

13.1.5cm.

14.4

15. Omit

16.

17. Complementary or equal

18. 180

19. 15

20.35

3.2 1. On a straight line. Connect and extend the delivery certificate.

22. Situation 1: Known:

Verification: (or)

Proof: In △ and △

△ △

that is

Case 2: Known:

Verification: (or)

Proof: In △ and △

,

△ △

23. prompt: OM=ON, OE=OD, ∠MOE=∠NOD, ∴△MOE≌△NOD, ∴∠OME=∠OND, DM=EN, ∠ DCM = \

(1) solution: equal to area

If the intersection is and the intersection is an extension line, then

Quadrilateral and quadrilateral are both squares.

(2) Solution: According to (1), the sum of the areas of all triangles in the outer ring is equal to the sum of the areas of all triangles in the inner ring.

The area of this path is square meters.