1. Multiple choice questions (3 points for each question, *** 18 points, please fill in the correct answer serial number in brackets after the question)
1. It is known that it is equal to ()
A. 1 B.- 1 C
2. As shown in figure □ABCD, ∠ c = 108, divided into equal parts ∠ABC,
Then ∠ABE= ()
A. 18
c . 72d 108
3. The quadrilateral with the length of () composed of two pieces of equilateral triangular paper is ().
A. isosceles trapezoid square rectangle diamond
4. In the picture below, what can overlap with the original picture after rotating 60 is ().
A. regular hexagon B. regular pentagon C. square D. regular triangle
5. As shown in the figure, in the isosceles trapezoid ABCD, AB//DC, AD=BC=8,
AB= 10, CD=6, then the area of trapezoidal ABCD is
16
c . 32d 16
6. Among the following conclusions, the wrong one is ()
① In ①Rt△ABC, given two sides are 3 and 4 respectively, and the length of the third side is 5;
(2) One side of the triangle is,, and if, then ∠ A = 90.
③ If ∠ A: ∠ B: ∠ C = 1: 5: 6 In △ABC, the triangle is a right triangle.
④ If it holds, then m = 4xy.
A.0 B. 1 C.2 D.3
Fill in the blanks (3 points for each small question, 36 points for * * *)
The square root of 7 is.
8. Factorization:
9. Calculation: =.
10. As shown in the figure, □ABCD and □EBCF are symmetrical about the line where BC is located.
∠ Abe = 90, then∠ F =.
1 1. As shown in the figure, ∠A=∠D, so △ABC and △DCB should be congruent.
The condition to be added is. (Write only one)
12. Calculation: =.
13. If the side length of a parallelogram is 6 cm and the circumference is 28 cm, then the side length here is cm.
14. As shown in the figure, in Rt△ABC, CD is the height on the hypotenuse AB, ∠ A = 60, and if AD= 1, the area of △ABC is.
15. Below, (1) parallelogram: (2) rectangle: (3) right trapezoid: (4) square; (5) equilateral triangle; (6) line segment. There are both axisymmetric figures and centrally symmetric figures. (Just fill in the serial number)
16. When the trapezoid in the above figure 1 meets the requirements, it can be translated, rotated and folded into Figure 2.
17. As shown in the figure, one side AD of ABCD is folded, point D falls on point F of BC, AE is the crease, and AB=8cm is known.
Bc = 10 cm. Then CE = cm.
18. As shown in the figure, the side length of the square ABCD is 8, m is on d, and DM=2, and n is the moving point of the AC side, then the minimum value of DN+MN is.
Three. Solution: (This big question is ***9 small questions, with a score of ***76. Write down the necessary calculation process, deduction steps or text description when answering. )
19. (5 points for each small question, *** 15 points)
(1) calculation:
(2) Simplify:
(3) Factorization:
20. (6 points for this question)
As shown in the figure, the straight line is ⊥m and the vertical foot is O. Please draw △ a ′ b ′ c ′ where △ABC is symmetrical about the straight line. Then draw a picture, where △ABC is symmetrical about point O. Please tell the positional relationship between △ A ′ B ′ C ′ and △.
2 1. (6 points for this question)
It is known that in □ABCD, the bisector of △ BCD intersects with AB at E, and the extension line of △ BCD intersects with DA at F;
Verification: AE=AF
22. (6 points for this question)
It is known that the quadrilateral ABCD is a diamond, and points E and F are the midpoints of sides CD and AD, respectively. If AE = 3 cm,
Find the length of cf.
23. (6 points for this question)
As shown in the figure: P is a point in the square ABCD, and the clockwise rotation energy of △ABP around point B coincides with △CBP'. If PB=5, find the length of PP'.
24. (7 points for this question)
In △AFD and △BEC, points A, E, F and C are on the same straight line, and there are four conclusions as follows:
( 1)AD = CB(2)∠B =∠D(3)AE = CF(4)AD//BC
Please use three of them as conditions and the other as a conclusion, make up a math problem and write the process of solving it.
25. (7 points for this question)
Please look at the following question: put the decomposition factor
Analysis: This binomial has neither a common factor nor a formula. What should we do?
Sophie,/kloc-a French mathematician in the 0/9th century? The popular grasp is that there are only two formulas, and they belong to the form of sum of squares. To use this formula, you must add a term and subtract it to get it.
People are remembering Sophie? Popular giving this solution is called "popular theorem". Please follow Sophie? The popular practice is to decompose the following factors.
( 1) (2)
26. (7 points in this question) In the known quadrilateral ABCD, BC=DC and diagonal AC bisector ∠ bad.
(1) because CE⊥AB, CF⊥AD, e and f are vertical feet respectively.
Proof: △ BCE △ DCF.
(2) If AB=2 1, AD = 9. BC = DC = 10.
Find the length of diagonal AC.
27. (Title, 8 points)
There are two trapezoidal experimental fields, and four different plants should be planted. Please divide each experimental field into two parts with the same area, and please explain your basis. (The two methods cannot be the same)
28. (8 points for this question)
Read the following passage: As shown in figure (1), △ABC is a right triangle, ∠ c = 90. Now make △ABC into a rectangle, so that the two vertices of △ ABC are two endpoints on one side of the rectangle, and the third vertex falls on the opposite side of the rectangle, then two rectangles that meet the requirements can be drawn: rectangle ACBD and rectangle AEFB[ as shown in Figure (2)].
Answer the question:
(1) Let the areas of rectangular ACBD and rectangular AEFB in the drawing be S 1 and S2 respectively, then S 1 S2 (fill in ">", "=" or "
(2) As shown in the figure, △ABC is an obtuse triangle. Fill in a rectangle according to the requirements in the article, and then you can draw a rectangle that meets the requirements. Draw it with Figure (3).
(3) As shown in Figure (4), △ABC is an acute triangle with three sides satisfying BC >; AC & gtAB, fill in a rectangle according to the requirements of the passage, and then you can draw a rectangle that meets the requirements. Draw it with Figure (4).
(4) Which rectangle in Figure (4) has the smallest circumference? Why?