First, multiple-choice questions (3 points for each question, ***30 points)
1. In physical education class, the teacher measured the long jump performance on the basis of ().
(a) The distance between parallel lines is equal; (b) The line segment between two points is the shortest.
(c) The two points of the shortest (d) vertical line segment determine a straight line.
2. As shown in figure 1, the method of drawing parallel lines of a known straight line through a point outside the straight line is given, based on ().
A the congruence angle is equal and the two straight lines are parallel. B the internal dislocation angles are equal and the two straight lines are parallel.
C the internal angles on the same side are complementary and the two straight lines are parallel. D. Two straight lines are parallel and have the same angle.
3. As shown in Figure 2, there are five patterns of "Fuwa Huanhuan". Which of patterns ②, ③, ④ and ⑤ can be obtained by translating pattern ① ()?
A.② B.③ C.④ D.⑤
4. (Hangzhou, 2008) As shown in the figure, if a straight line is known, then ()
(A) (B) (C) (D)
5. If ∠ α and ∠βare diagonal and complementary, the straight lines on both sides of them ().
A. mutually perpendicular B. mutually parallel C. neither perpendicular nor parallel D. uncertain
6. As shown in Figure 3, if ∠ 1 = 70, ∠ 2 = 1 10 and ∠ 3 = 70, there is ().
A.a ∨ b.b.c ∨ d.c.a. ⊥ d.d. Neither of them can judge whether they are parallel.
7. In the Chinese characters "Wang, Man, Wood, Water, Mouth and Reason", () can be translated into new Chinese characters.
1。
8. Put a pair of triangular wrenches as shown in Figure 4. If the degree of ∠ 1 is 54 degrees greater than that of ∠2, then ∠ 1 = ()
A. 18
9. In math class, some students drew the following four kinds of figures when practicing the vertical line with point B as the line segment AC. Please count it. The number of errors is ().
1。
10. As shown in Figure 6, ∠ 3 = ∠ 4 is known. If ∠ 1 = ∠ 2, you need ().
A.∠ 1 =∠3b .∠2 =∠3c .∠ 1 =∠4d . AB∨CD
Fill in the blanks (3 points for each question, 30 points for * * *)
1 1. As shown in Figure 7, when the scissors mouth ∠AOB increases by 2 1, ∠COD increases.
12. After the graphics are translated, the following features will not change _ _ _ _ _ (fill in all serial numbers you think are correct). (1) the shape of the graphics; (2) the position of the graph; ③ the length of the line segment; ④ the size of the angle; ⑤ Vertical relation; ⑥ Parallel relationship.
13. as shown in fig. 8, if ∠ 1 = 40 and ∠ 2 = 100, then the congruence angle of ∠3 is equal to _ _ _ _ _ _ _ _ _ _.
14. As shown in Figure 9, if a piece of paper with the same width is folded as shown in the figure, then _ _ _ _ _ _ _ _ _.
15. When the straw sucks the beverage out of the can, as shown in figure 10, then (the top surface and bottom surface of the can are parallel to each other).
16. A cargo ship sailed in the northwest direction of 62, then turned right 28 and left 28 to avoid the reef. At this time, the cargo ship along the direction of _ _ _ _ _.
17. Three sticks can be used to form the Chinese character "gan". Please move the stick to make it another Chinese character, and write the Chinese character you get: _ _ _ _ _ _ _ (write only one).
18. As shown in figure 1 1, CD⊥AB is in D, de∨BC, ∠ 1 = ∠ 2, then the positional relationship between FG and AB is _ _ _ _ _.
19. For three straight lines in the same plane, the following five conclusions are given: ① ∨; ② ∥ ; ③ ⊥ ; ④ ∥ ; ⑤ ⊥. Take two of them as conditions and one as a conclusion, and form a proposition that you think is correct: _ _ _ _ _ _ _ _ _ _ _ _ _.
20. As shown in figure 12, the pattern 1 consists of black and white regular hexagonal floor tiles. The second and third patterns can be regarded as the translation of 1 pattern, so (1) there are _ _ _ _ _ _ _ _ white hexagonal floor tiles in the fourth pattern.
Iii. Answering questions (***60 points)
2 1. (6 points in this question) As shown in figure 13, the AB edge of △ABC is moved to EF after translation.
Can you give two methods to make a translation triangle? Please express it.
22. (6 points in this question) As shown in figure 14, AB∑CD, what conditions need to be added?
Can ∠ 1=∠2 hold? (Name at least two names)
23. (7 points in this question) As shown in figure 15, it needs to be judged.
(1) There are three sections that can be considered, namely _ _ _ _ _ _ _ _ _ _ _ and _ _ _ _ _ _ _.
(2) When WEDM is considered, only the congruence angle is equal to _ _ _ _ _ _ _ _ _ _ _,
Or _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
24. (7 points in this question) As shown in figure 16, the points D, E and F are on AB, BC and AC respectively, and DE∨AC and EF∨AB are recorded as follows: ∠ A+∠ B+∠ C = 65438+.
Because DE∨AC, AB∨EF, ∠ 1 =∞,
∠3=∠ .( )
Because AB∨EF, ∠2 =∞_ _. ()
Because DE∑AC, ∠4 =∞_ _. ()
So ∠ 2 = ∠2=∠A (equivalent substitution).
Because ∠ 1+∠ 2+∠ 3 = 180, ∠ A+∠ B+∠ C = 180 (equivalent replacement).
25. (8 points for this question) As shown in figure 17, a square piece of land with a side length of 8 meters has two roads built on it.
The width is 2 meters, and various flowers and plants are planted in the blank part. Please find out the area of flowers and plants with the knowledge of translation.
26. (8 points for this question) As shown in figure 18, there is a mountain between A and B, and there is a highway between A and B.
Geographically, the direction of the highway is northwest11132'. If a and b start at the same time, then
How many degrees is the construction of B according to the northeast, so that the highway can be accurately connected halfway up the mountain? Why?
27. (9 points in this question) As shown in figure 19, it is a rectangular plate (opposite to AB∨CD and AD∨BC, all four corners are right angles). Master Wang is now looking for the little E on AB to do ∠ AEC = 150.
(1) Please write down the method of determining point E in combination with the drawings, and draw point E in the drawings;
(2) Briefly state your reasons again.
28. (9 points in this question) It is known that the plan of a certain brand of stainless steel cone is shown in Figure 20, and the design requirement is AB∨CD, and ∠ A = ∠ C =.
143, please help the designer to calculate the degree of ∠E and explain the reasons.
Reference answer:
1. 1，c； 2、A； 3、D； 4、C； 5、A； 6、A； 7、D； 8、C； 9、D； 10、d。
Second, 1 1, 21; 12、①③④⑤⑥; 13、 , , ; 14、 ; 15、70; 16,62 north by west; 17, undergraduate or local; 18、fg⊥ab； 19, the answer is not unique, just reasonable and correct; 20、
Three, two1. Give the following two ways:
(1) According to the fact that the translated graph is parallel to the corresponding line segment of the original graph, there should be ED∨AC and FD∨BC.
(2) Similarly, according to the parallel and equal line segments connected to the corresponding points after translation, AE is connected so that CD∑AE and CD=AE.
22. Condition1:; Condition 2: The bisectors of and are respectively.
23.( 1) , ; (2) , ;
24.∠ C, ∠B, two straight lines are parallel and have the same angle, ∠4, two straight lines are parallel and have the same internal dislocation angle, ∠A, two straight lines are parallel and have the same angle.
25. 16
26. If the construction is carried out at 68 28' north-east of Area B, the highway can be accurately connected on the mountainside. Because the road directions of A and B should form a straight line and a right angle.
27. Solution: (1) Take CD as the starting edge, use a protractor to make ∠ DCE = 30, and the rays CE and AB intersect at point E, then point E is the point you are looking for.
(2) Because AB∥CD, ∠ DCE+∠ AEC = 180, because ∠ DCE = 30 (made).
So ∠ AEC =180-∠ DCE =150.
28. solution: if e is EF∨AB,
Because AB∨CD, EF∨CD, and because A = ∠ C = 143,
Therefore, ∠ AEF = 180-∠ A = 37 (two lines are parallel and complementary angles of each other).
So ∠ CDF = 180-∠ C = 37 (the complementary angles of two parallel lines are internal angles).
So ∠ e = ∠ AEF+∠ CDF = 74.