(Examination time: 120 minutes, full mark: 120 minutes)
1. Multiple choice questions (* * 12 questions, 3 points for each question, ***36 points. Only one of the four options given in each question meets the requirements. Please fill in the serial number of the correct answer in the brackets after the corresponding question.
1. The following figures are the station emblems of Guilin, Hunan, Gansu and Foshan TV stations, among which the axisymmetric figure is ().
2. For the height of any triangle, the following statement is incorrect ()
A. An acute triangle has three heights. B. A right triangle has only one height.
C. Any triangle has three heights. D. an obtuse triangle has two heights outside the triangle.
3. If two sides of a triangle are 3 and 8 and the third side is odd, then the third side is () A. 5 or 7 B. 7 or 9C.7D.9.
4. An angle of an isosceles triangle is 80, so its base angle is ().
A.50 b.80 c.50 or 80 d.20 or 80
5. The coordinate of the point where point M (3 3,2) is symmetrical about Y axis is (). a .(-3，2) B.(-3，-2) C. (3，-2) D. (2，-3)
6. As shown in the figure, ∠ b = ∠ d = 90, CB=CD, ∠ 1 = 30, then ∠2= (). 30 BC to 40 BC
7. There are four sticks with lengths of 4cm, 6cm, 8cm and 10cm respectively. The number of sticks that can form a triangle is ().
A. 1 B.2 C.3 D.4 8。 As shown in the figure, in △ABC, AB=AC, D is the midpoint of BC, and the following conclusions are drawn: (1) △ Abd △ ACD; (2)ad⊥bc；
(3)∠B =∠C； (4)AD is the angular bisector of △ABC. The correct one is ().
A. 1 B. 2 C. 3 D.4
9. As shown in the figure, in △ABC, AC = AD = BD, ∠ DAC = 80? , so the degree of ∠B is () A.40? B.35？ C.25？ D.20？
10. If each inner angle of a polygon is equal and the sum of the inner angles is 1800, the outer angle of the polygon is ().
.30 caliber? B.36？ C.60？ Cao 72
1 1. As shown in the figure, a classmate accidentally broke a triangular piece of glass into three pieces, and now he wants to go to the glass shop to match an identical piece of glass, so the most convenient way is to take ().
A. 1b.2c.3d.① and ②
12. Use regular triangles, regular quadrangles and regular hexagons to spell out the patterns as shown in the figure, that is, starting from the second pattern, the number of regular triangles in each pattern is four more than that in the previous pattern. Then the number of regular triangles in the nth pattern is () (represented by an algebraic expression containing n).
A.2n+ 1 B. 3n+2 C. 4n+2 D. 4n-2
2. Fill in the blanks (this big question is ***6 small questions, each with 3 points, *** 18 points. Please fill in the answer on the line after the corresponding question)
13. if the symmetry point of A(x, 3) about the y axis is B (-2, y), then x = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
14. As shown in the figure: Δ δABE?δACD, AB= 10cm, ∠ A = 60, ∠ B = 30,
Then ad = _ _ _ _ cm and ADC = _ _ _.
15. As shown in the figure, it is known that line segment ∠A=∠B and CD intersect at point O, and ∠ A = ∠ B. Just add a condition _ _ _ _ _ _ _ _ _, and there is △ AOC △ BOD. 16. As shown in the figure, straight lines A, B and C represent three expressways. Now, if you want to build a cargo transfer station, you need to be at the same distance as the three highways, and there are places to choose from.
17. As shown in the figure, ≈A+≈b+≈C+≈D+≈E+≈F+≈G =
18. As shown in the figure, Liang Xiao started from point A 10m, turned right 15, went forward 10m, turned right 15 ... So he continued to walk, and when he returned to the starting point A for the first time, he left M.
Third, answer the question (this big question is ***8 small questions, ***66 points)
19. (6 points in this question) The sum of the inner angles of a polygon is 180 less than three times the sum of its outer angles. What are the sides of this polygon?
20 (8 points in this question) It is known that points B, E, C and F are on the same straight line, AB = DE, ∠ A = ∠ D, AC∨DF. Verification: (1) △ ABC △ def; ⑵ Be = cf.2 1。 (8 points in this question) As shown in the figure, in △ABC, AB=AC=CD, BD=AD,
Find the degree of each angle in △ABC.
22. (8 points for this question) The position of △ABC in the plane rectangular coordinate system is shown in the figure. A.
There are three points on the grid, b and C.
(1) Let △ A1b1of △ABC be symmetrical about X, and write the coordinates of point C 1; (2) Make △A2B2C2, make △ABC symmetrical about Y, and write the coordinates of point C2.
23. (8 points in this question) As shown in the figure, point B and point C are points on both sides of ∠MAN, and AB = AC.
(1) Draw according to the following statement: (No writing method is required, and drawing traces are reserved) ① AD⊥BC, and the vertical foot is D;
② The bisector CE of ②BCN and the extension line of AD intersect at point E; ③ connect BE.
(2) Do not add line segments and letters after (1).
Please write two pairs of congruent triangles except △ Abd △ ACD:,; And choose a pair of congruent triangles to prove it. 24. (8 points in this question) As shown in the figure, AD is the center line of △ABC and BE is the center line of △ABD.
(1) ∠ Abe = 15, ∠ bad = 40, find the degree of ∠BED; (3) If the area of △ABC is 40 and BD=5, what is the distance from E to BC?
25. (this question 10) As shown in the figure, point B is on the AC line and point E is on the BD line.
∠ AB=DB =∠ DBC, AB=DB, EB = CB, M, N are the midpoint of AE and CD respectively. Try to explore the relationship between BM and BN and prove your conclusion.
26. (This question 12 points) As shown in the figure, it is known that E is a point on the bisector of ∠AOB, EC⊥OB, ED⊥OA, C and D are vertical feet, and the CD is connected to the OE at point F.
Verification: OE is the middle vertical line of CD.
(2) If