1. Move the graph along _ _ _ for a certain distance in the plane, and such graph movement is called translation. Translation does not change the _ _ _ _ _ _ and _ _ _ _ of the graph.

Note: 1, provided that the object moves on a curved surface in the same plane, it is not called translation.

2, must be in the same direction.

3. Graphic translation is determined by the direction and distance of translation.

Knowledge point 2. The essence of translation

2. After translation, _ _ _ _ _ _ _ and _ _ _ _ are equal respectively.

A line segment connected to the corresponding point _ _ _ _ _ _ _ _.

basic skill

1. The following phenomena: ① the lifting movement of the elevator; ② The plane glides along a straight line on the ground;

(3) the rotation of windmills, (4) the rotation of automobile tires. Among them, () belongs to the translation.

A.②③B、②④C.①②D.①④

2. As shown in the figure on the left below, after translating △ABC to △DEF, there are the following statements:

①AB∑DE，AD = CF = BE②∠ACB =∠DEF；

③ The direction of translation is from point C to point E;

④ The translation distance is the length of the line segment BE.

Among them, the statement is correct ()

A.B.2 C.3 D.4

3. As shown in the figure on the right below, in the equilateral △ABC, D, E and F are the midpoints of BC, AC and AB respectively, then △AFE can be obtained by translation ().

A.△DEFB。 △FBDC。 △EDCD。 △FBD and△ △EDC

4. The following figure belongs to the translation position transformation is ().

5. In the figure below, (1) is () only by translation.

6. As shown in the figure, after translating △ABC, △ A ′ B ′ C ′ is obtained, and the positional relationship between line AB and line A ′ B ′ is as follows.

7. In the question1,the line segment parallel and equal to line segment AA' is.

8. Move the line segment with a length of 5cm upward by 10cm, and the length of the line segment is ().

A, 10cmB, 5cmC, 0cmD, uncertain.

Learning is a process of consolidating while learning new knowledge. In order to make progress, we must practice what we have learned more. Therefore, the editor compiled the third unit of mathematics in the second volume of grade two for your reference.

Fill in the blanks

1, the translation, rotation and axis symmetry of the graph have the same properties as _ _ _ _ _ _.

2. After translation, the line segment is connected to the corresponding point _ _ _ _ _ _ _ _ _.

3. After rotation, the distance from the corresponding point to the rotation center is _ _ _ _ _ _ _.

At 9: 30, the angle between the hour hand and the minute hand of the clock is _ _ _ _ _.

5. An equilateral triangle rotates at least _ _ _ _ degrees around the intersection of its three sides, and can coincide with itself.

6. The square ABCD with a side length of 4cm rotates around its vertex A 180, and the length of the route passed by vertex B is _ _ _ _ _ cm.

7. If A diagram is shifted up by 2 units to get B diagram, left by 2 units to get C diagram and down by 2 units to get D diagram, then D diagram can be shifted by _ _ _ _ _ _ units to get A diagram.

8. If △ABC and △DCE are equilateral triangles, then in this figure,

△△ ace can be obtained by rotating around a point.

Third, solve the problem (Figure 8)

1. After translation, the AB side of △ABC moves to EF to make a translation triangle.

2. As shown in the figure, in the grid with the side length of 1, make a graph in which △ABC rotates 90 counterclockwise around point A and then translates 2 squares downward.

3. As shown in the figure, in the plane rectangular coordinate system,,,.

① Calculation area.

② Make a graph △A2B2C2, translate it down by 1 unit, and then translate it to the left by 2 units.

(3) Take A as the center of rotation △ABC rotates 900 counterclockwise and then draw△ △A3B3C3.

4. In the grid as shown in the figure, the vertices of each small square with a side length of 1 and △ABC are all on the grid. After the plane rectangular coordinate system is established, the coordinate of point B is (-1, 2).

(1) Translate △ABC down by 8 units to get the corresponding △, draw △ and write the coordinates.

(2) Take the origin o as the center of symmetry, draw a δ which is symmetrical with the origin o, and write the coordinates of this point.

5. As shown in the figure, it is known that ∠ EAD = 32, and △ADE can coincide with △ABC after rotating 50 around point A, and the degree of ∠BAE can be obtained.

6. The quadrilateral ABCD is a square. Delta △ADF is rotated by one or four fixed angles to get Delta △ABE. As shown in the figure, if AF=4 and AB=7, find (1) to indicate the rotation center and rotation angle. (2) Find the length of DE. (3) What is the positional relationship between 3)BE and DF?

7. As shown on the right, △ABC is a right triangle and BC is the hypotenuse. After rotating △ABP counterclockwise around point A,

Can coincide with △ACP', if AP=3, find the length of PP'.

8. Place two right-angle triangular plates (∠ BAC = ∠ B' A'C = 30) with the same size as shown in the figure (1), fix the triangular plate A'B'C, and then rotate the triangular plate ABC clockwise (the rotation angle is less than 90) around the right-angle vertex C to the figure.

(1) verification: △ BCE △ b ′ cf;

(2) When the rotation angle is equal to 30, is A'B' perpendicular to A' b'? Please explain the reason.

9. As shown in the figure, O is the center of the regular hexagon ABCDEF, and △OBC translation in the figure below can get ().

A.△CODB。 △OABC。 △OAFD。 △OEF

10. Translate the isosceles right angle △ABC with an area of 12cm2 by 20cm to the upper right to get △MNP, then △MNP is a triangle with an area of cm2.

1 1. As shown in Figure 7, the quadrilateral EFGH is translated from the quadrilateral ABCD.

Given AD=5 and ∠ b = 70, then ()

A.FG=5，∠G=70 B.EH=5，∠F=70

C.EF=5，∠F = 70D。 EF = 5，∠E=70

13, (20 13 Chenzhou, Hunan) is in the illustrated grid paper.

(1) Make a graph of △ABC symmetry about MN △ A1b1c1; (2) Explain how △A2B2C2 is translated from △A 1B 1C 1

Second, the rotation of graphics:

Knowledge point one, the definition of rotation.

On the plane, _ _ _ _ _ _ _ _ _ _ _ _ _ refers to

Knowledge point 2, the nature of rotation

1. The line segment and the corresponding angle of the rotated graph corresponding to the original graph are _ _ _ _ _ _ _.

2, the distance from the corresponding point to the center of rotation _ _ _ _

3._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4. After rotation, every point on the graph rotates around the rotation center at the same angle and direction.

To understand the concept of rotation, we should pay attention to the following two points:

(1) Rotation, like translation, is the basic transformation of graphics.

(2) The decisive factors of graphic rotation are rotation center, rotation angle and rotation direction.

basic skill

1, which belongs to rotation in the following movements is ()

A, the rolling of basketball in the rolling process B, the swinging of the pendulum of the clock

C, the movement of the balloon in the air D, the process of folding a figure in half along a straight line.

2. Rotate the graph 900 clockwise, and the graph is ().

Accelerated business collection and delivery system (adopted by the United States post office)

3. (Shantou, Guangdong, 20 12, 4 minutes) As shown in the figure, rotate △ABC clockwise by 50 degrees around point C to get △ A ′ B ′ C ′. If < a = 40. ∠B'= 1 10, then ∠.

A. 1 10 B.80 C.40 D.30

4.(20 13 Putian) As shown in the figure, rotate Rt△ABC (where ∠ B = 35 and ∠ C = 90) clockwise around point A to the position of △AB 1C 1.

5. (Guangzhou, 20 12) As shown in the figure, in the equilateral triangle ABC, AB=6, D is a point on BC, BC=3BD, and△ △ABD rotates around point A to get△ △ACE, then the length of CE is.

6. As shown in the figure, △ABC is an isosceles right triangle, and BC is the hypotenuse. After rotating △ABC counterclockwise around point A, it can coincide with △ACP'. If AP=3, then the length of PP' is equal to.

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7. As shown in the figure, E and F are points on BC side and CD side of square ABCD, and BE=CF, connecting AE and BF. Rotate △ABE to △BCF counterclockwise around the center of the square, and the rotation angle is a (0

8. When the minute hand and the hour hand on the clock have passed 20 minutes, the rotation angles of the hour hand and the minute hand of the clock are () degrees respectively.

A 10 and 20B 120 and 20C 120 and 10D20 and 10.

9.(20 13 Qinzhou, Guangxi) As shown in the figure, in the plane rectangular coordinate system, all three vertices of △ABC are on the grid point, and the coordinate of point A is (2,4). Please answer the following questions:

(1) Draw △A 1B 1C 1 of the axis symmetry of △ABC about X, and write the coordinates of point A 1.

(2) Draw △A 1B 1C 1 and rotate around the origin o 180, and write down the coordinates of point A2.

10.(8 points) (20 13 Huaian) As shown in the figure, point A, point B and point C are all grid points in two squares with side length of 1 unit.

(1) shift △ABC to the left by 6 unit lengths to get △ a1b1c1;

(2) Rotate △ABC counterclockwise around point O 180 to get △A2B2C2. Please draw △A2B2C2.

1 1. Rotate the square ABCD clockwise around point A to get the square AEFG, and the sides FG and BC intersect at point H (as shown in the figure). (1) Is the line segment HG equal to the line segment HB? Please observe the conjecture first, and then prove your conjecture.

Central symmetry

Knowledge point 1. The Concept of Centrally Symmetric Graph

In a plane, if a figure can coincide with itself after rotating around a certain point by180, then this figure is called a centrosymmetric figure. This point is its center of symmetry.

(If a graph is folded in half along a straight line and the two parts completely overlap, such a graph is called an axisymmetric graph. This straight line is called the axis of symmetry)

Knowledge point 2. Properties of Centrally Symmetric Graphs

The line segments connected by each pair of corresponding points on the central symmetric figure are equally divided by the symmetric center.

Knowledge point 3. Difference between Axisymmetric Graphics and Centrally Symmetric Graphics

Axisymmetric figure

A straight line with an axis of symmetry has a center point of the axis of symmetry.

Fold in half along the symmetry axis and rotate around the symmetry center 180.

Folding in half overlaps with the original drawing, and rotating 180 overlaps with the original drawing.

basic skill

1, (20 13 Liupanshui, Guizhou, 4,3 points) Among the following figures, the axis symmetry is ().

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2. (20 13, Hebei Province, 3,2 points) Which of the following figures is both axisymmetric and centrally symmetric?

3. (20 13 Harbin City, Heilongjiang Province 3) Among the following figures, () is both axisymmetric and centrally symmetric.

4.(3 points) (20 1 1 Guilin) The following figures are the TV station emblems of Guilin, Hunan, Gansu and Foshan respectively, in which () is a central symmetrical figure.

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5.(20 13 Chenzhou, Hunan) Among the following patterns, the one that is not centrosymmetric is ().

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6.(20 13 Taian,1,3 points) In the unit square grid as shown in the figure, △ABC is translated to get △ A1b1,and it is known that a point P (2.4) on AC.

A.( 1.4，- 1)B.( 1.5，2)C.( 1.6， 1)D.(2.4， 1)

7. (Hangzhou, 20 13, 3 points) Among the following "Yan characters", the one that belongs to the axisymmetric figure is ().

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8. (Suining, Sichuan, 20 13) The following patterns are composed of regular polygons, of which () is both axisymmetric and centrally symmetric.

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9. (Shandong Yantai 20 13) The following are four signs: recycling, green packaging, water saving and low carbon, among which () is a centrally symmetric figure.

10. (Nanchang, Jiangxi, 20 13) As shown in the figure, rotate △AD⊥BC counterclockwise around point A for a certain angle to get △ADE. If ∠ CAE = 65, ∠ E = 70 and AD ∠ BC, ∠BAC is (.

60-75 AD

1 1. (Mianyang, Sichuan 20 13) As shown in the figure, put the smiling face "QQ" in the rectangular coordinate system, and it is known that the coordinates of the left eye A are (-2,3), and the coordinates of the lip point C are (-1, 1).

12.(20 13 Anshun, Guizhou) As shown in the figure, in the plane rectangular coordinate system, the line segment AB is obtained after rotating 90 counterclockwise around point A, and the coordinates of this point are.

13. (Liangshan Prefecture, 20 13) As shown in the figure, △ABO and △CDO are symmetrical about the center of point O, and points E and F are on line AC, and AF=CE.

Proof: FD=BE.

This math test and answer in the second volume of the second grade of junior high school are shared here for everyone. I hope it will help everyone!

Unit 3, Volume 2 of Mathematics in Grade 2: The unit exercises compiled here cover all aspects of the content of regular exams. Let's practice hard and consolidate what we have learned.

1. Multiple choice questions: (5 points for each question)

1. Among the following equations about x, the one that belongs to the fractional equation is ().

a . 3x = 12 b . 1x = 2c . x+25 = 3+x4 d . 3x-2y = 1

2. The following calculations are correct ()

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3. The following are true ()

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4. Solve the equation and remove the denominator ()

A.B

CD。

5. The result of simplification is ()

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6. If the score is 0, () A.B.C.D

7. If is, the value of is () A.B.C.D

2. Fill in the blanks: (5 points for each question)

9. Choose any two of the following three non-zero formulas to form a score, and the result of simplifying this score is.

10. The diameter of the cold virus is 0.00000034 meters, which is _ _ _ _ _ _ _ _ _ _ _ meters by scientific notation;

1 1. The calculation result is _ _ _ _ _ _ _.

12. If the fractional equation about x has no solution in the real number range, then the real number A = _ _ _ _ _ _

13. If known, then.

Three. Answer: (7 points for each question)

14. Simplify:

15. Calculation:

18. Please simplify the following formula first, and then choose a number you like to make the original formula meaningful for evaluation.

This is the end of the third unit test in the second volume of junior two mathematics. I hope it will help everyone!