First, multiple-choice questions (3 points for each small question, 36 points for * * *)

1, the following six figures are axisymmetric figures ().

1。

2, can determine the congruence of two right triangle condition is ()

A. the hypotenuse is equal. B. Two right angles are equal. C. an acute angle is equal to. The two acute angles are equal.

3. The result of simplification is ()

A.B. C. D。

4. If the equation has an increasing root, then the value of is ()

A.0 B.- 1 C.3 D. 1

5. Class A and Class B go for an autumn outing in the park 15km away from school. Two classes start at the same time. The speed of Class A is 1.2 times that of Class B, and it turns out to be half an hour earlier than Class B. What is the speed of each class? If the speed of class B students is km/h, then the equation is listed according to the meaning of the question, and ()

A.B.

C.D.

6, in the following statement, belongs to the proposition is ()

A. The perpendicular line as a line segment B. Are the complementary angles of equal angles equal?

C. A triangle is an axisymmetric figure D. Make a triangle with three line segments.

7. As shown in the figure, in △ABC, D and E are the midpoint of BC and AC respectively, BF bisects ∠ABC, and intersects d E at point F. If BC=8, the length of DF is

a2 b . 3 c . d . 4

8. As shown in the picture, the triangle in Xiaoying's book was polluted by ink, and soon he drew a triangle exactly like the one in the book according to what he had learned, so the basis for the two triangles to be exactly the same is ().

A. Social Service Bureau

9. As shown in the figure, in the equilateral triangle ABC, BD = CE, AD and BE intersect at point P,

So the degree of ∠APE is ()

45 BC to 55 BC

10, as shown in the figure, point P is within ∠AOB, point M and point N are symmetrical points of point P about straight lines OA and OB respectively, and line segment MN intersects OA and OB at points E and F. If the circumference of △PEF is 500px, the length of line segment MN is ().

A2.5px b.500px c. is between 250px and 500px D, uncertain.

1 1. If the average value of a set of data,, and is 8 and the variance is 2, then the average value and variance of a new set of data 2, 2,, and 2 are () respectively.

A.8 and 2 B. 16 and 4 C. 16 and 8 D. 6 and 16.

12, as shown in the figure, in △ABC, AD⊥BC is in D, BE⊥AC is in E, and AD is in EF.

If BF=AC, ∠ABC equals ()

45 BC to 48 BC

Fill in the blanks (3 points for each small question, *** 15 points)

13. The point with the same distance to the three vertices of the triangle is, and the point with the same distance to the three sides is.

14, in the school hygiene inspection, it is stipulated that the classroom hygiene score of each class accounts for 30%, the environmental hygiene score accounts for 40%, and the personal hygiene score accounts for 30%. Class 1, Grade 8 got 85 points, 90 points and 95 points respectively, so the total score of class health examination is _ _ _ _ _ _ _ _ _ _ _.

15, when x=, the value of the fraction is 1.

16, observe the given score:, guess and explore the law, the 10 th score is _ _ _ _ _ _ _, and the nth score is.

17, as shown in the figure: in △ABC, AD=AE, BD=EC, ∠ ADB = ∠ AEC = 105, ∠ B = 40,

∠CAE =；

Iii. Answering questions (***69 points)

18, (5 points) As shown in the figure, OM and ON are two expressways, and A and B are two factories. Now we're going to build a warehouse P in ∠ OM, ON, so the distance to the two roads is equal, and the distance to the two factories is equal. Please confirm the location of warehouse P (no words, leaving traces of drawings).

19, calculation (5 points for each small question, *** 10)

( 1) (2)

20.(8 points) Simplify first, and then find the value at that time.

2 1, solve the fractional equation (6 points for each small question, *** 12 points)

( 1) (2)

22.(8 points) The solution of equation ① is

② The solution is

The solution of ③ is x=.

④ The solution is

(1) Write the 5th and 6th equations and their solutions directly according to the law you found.

⑤________________ .。 ⑥______________

(2) Please use an equation containing a positive integer n to express the above law and find its solution.

23.(6 points) As shown in the figure, ∠BAC=∠DAE, ∠ABD=∠ACE, AB=AC. Verification: BD=CE.

24.( 10) After the realization of the "three links" between the two sides of the Taiwan Strait, the cost of purchasing apples from Taiwan Province Province by a fruit sales company dropped significantly. Please work out the cost of buying apples from Taiwan Province Province before realizing the "three links" according to the conversation between the two managers.

25.( 10) As shown in the figure, the bisectors of ∠ABC and ∠ACB intersect at F, and if they intersect at F, they are DE//BC, AB at D and AC at E. 。

It is proved that (1)△BDF is an isosceles triangle;

(2)BD+EC=DE。