Zibo city seventh grade second volume mathematics review key plus questions

Seventh-grade Mathematics People's Education Edition always reviews the learning plan at the end of next semester

Examination contents

Chapter V Intersecting Lines and Parallel Lines Chapter VI Plane Rectangular Coordinate System

Chapter VII Triangle Chapter VIII Binary Linear Equations

Chapter IX Inequality and Inequality. Formula Group Chapter 1 Data Collection, Arrangement and Description

Chapter 15 algebraic expression's Multiplication, Division and Factorization

Chapter 5 Intersecting Lines and Parallel Lines

(1) Knowledge Structure Diagram of this chapter:

(2) Examples and exercises:

1. Diagonal angles and adjacent complementary angles: 1. As shown in the figure, ∠1 and ∠2 are the figures with opposite corners ()

A.1 B.2 C.3 D.4

2. As shown in Figure 1-1, straight lines AB, CD and EF all pass through point O,

There are several pairs of opposite corners in the figure. ()

3. as shown in figure 1-2, if ∠AOB and ∠BOC are a pair of adjacent complementary angles, OD divides ∠AOB,

OE is inside ∠BOC, and ∠BOE= ∠COE, ∠ doe.

find the degree of ∠COE. ()

Second, the vertical line:

Known: As shown in the figure, there are two villages A and B on both sides of a highway.

<; 1> At present, the township government serves the people, and buses are opened along the highway, and a bus station P is built along the roadside. At the same time, roads from the station P to the villages of A and B are built, and the sum of the roads to be built is required to be the shortest. Please design the location of the station, draw the location of point P in the map, and explain the truth in one sentence on the back horizontal line ...

< 2> In order to facilitate motor vehicle travel, Village A plans to build a motor vehicle-only road directly from the village. Can you help Village A save money and design the shortest road? Please draw the shortest road you designed and built in the picture, and explain the truth in one sentence on the back horizontal line ...

III. Judgment of congruent angle, internal dislocation angle and internal angle on the same side

1. As shown in Figure 3-1, according to the position of each angle, The following judgments are wrong: ()

(A)∠1 and ∠2 are homolateral internal angles; (B)∠3 and ∠4 are internal angles; www .xkb 1.com

(C)∠5 and ∠6 are homolateral internal angles (D

if AB∥CD, then ∠ = ∠.

2. It is known that the two sides of two angles are parallel, one of which is 52, AB∥CD the other is _ _ _ _ _ _.

3. Among the eight angles generated when two parallel straight lines are cut by a third straight line, the two angles whose bisectors are parallel to each other are ()

A.

try to write down all possible situations and explain the reasons.

5. as shown in figure 4-3, EF⊥GF, vertical foot is f, ∠ AEF = 15,

∠ DGF = 6. Try to judge the position relationship between AB and CD, and explain the reasons.

6. as shown in figure 4-4, AB∥DE, ∠ ABC = 7, ∠ CDE = 147, find the degree of ∠ C. ()

7. as shown in figure 4-5, CD∥BE, then ∠. What is the degree of ∠1? ()

8. as shown in figure 4-6: ab ∥ CD, ∠ABE=∠DCF, verification: be ∥ cf.

5. Application of parallel lines:

1. Someone started from point A, walked 1 meters to the north-east direction, and arrived. Then ∠ABC is equal to ()

A.45 B.75 C.15 D.135

2. A student practiced driving a car and found that after turning twice, the driving direction was the same as the original direction. The turning angles of these two times may be ()

A turning 5 to the right for the first time. Turn right for the second time 5

c Turn left for the first time 5, turn left for the second time 13

d Turn right for the first time 5, turn right for the second time 5

3. As shown in Figure 5-2, after a rectangular piece of paper is folded along EF, points D and C fall at the positions of D' and C' respectively, < (unit: cm)

5. As shown in (Figure 6-2), it is known that the side length of a large square is 1 cm and the side length of a small square is 7 cm.

Find the shaded area. (Results reserved)

6. Find the area (unit: cm) of the shaded part in (Figure 6-3)

7. Among the following propositions, the number of true propositions is ()

① The complementary angle of an angle may be acute;

② The distance between any point on two parallel lines and another parallel line is the distance between these two parallel lines;

③ In the plane, there is one and only one straight line perpendicular to the known straight line;

④ In the plane, there is one and only one straight line parallel to the known straight line;

a.1b.2c.3d.4

8. Known: as shown in Figure 8-1, AD BC, EF BC, 1= 2.

verification: ∠CDG=∠B.

9. Known: as shown in Figure 8-2, AB∥CD, 1= 2, ∠ E = 65 2', find the degree of ∠ F.

1. as shown in figure 8-3, AE⊥BC, FG⊥BC, ∠1=∠2, ∠D =∠3+6? , ∠CBD=7? .

(1) verification: ab ∥ CD; (2) find the degree of ∠ C. ()

11. As shown in Figure 8-4, in the rectangular ABCD, ∠ ADB = 2. Now fold this rectangular piece of paper along AF. If

AB' ∥BD is used, what is the included angle ∠BAF between the crease AF and AB? ()

12. As shown in Figure 8-5, point B is 3? north-west of point A? Direction,

1 meters from point A, and point C is 6 east-north of point B? , ∠ACB = 4?

(1) Find the distance from point A to line BC; (1m)

(2) Q: How many degrees is point A west of point C?

(Write down the calculation and reasoning process) ()

13. As shown in the figure, in the square grid of, the side length of each small square is 1 unit, and it will be translated down by 4 units, so please draw it (drawing is not required).

VI. Drawing by equal product transformation:

1. As shown in figure △ ABC, passing through point A. Can you make a straight line EF through a point E on the side of AB, so that it can also divide this triangle into two parts with equal areas?

2. There is a piece of cultivated land with the shape as shown in the figure. Two brothers want to divide it into two equal parts. Please design a plan to divide it into the required number of parts. If only one straight line is allowed, can you do it?

3. as shown in the figure, how to draw a line if you want to straighten a broken road MPN in the middle of a square piece of cultivated land, but you can't change the size of cultivated land on both sides of the broken road?

4. It is known that, as shown in the figure, the pentagonal ABCDE is made into a triangle with a triangle ruler and a ruler, so that the area of the triangle is equal to that of the given pentagonal ABCDE.

Chapter VI Plane Cartesian Coordinate System

(1) Knowledge structure diagram of this chapter:

(2) Examples and exercises:

1. Fill in the blanks:

1. Known point P(3a-8, a-1).

(1) Point P is on the X axis, then the coordinates of point P are

(2) point p is in the second quadrant, and a is an integer, then the coordinate of point p is;

(3) If the coordinate of Q is (3, -6) and the straight line PQ∥x axis, the coordinate of P is.

2. In the chessboard as shown in the figure, if Shuai

is located at point (1,-2), the phase is located at point (3, p >. The coordinates of the symmetrical point of the point about the axis are; The coordinate of the point symmetrical to the coordinate origin is.

4. If it is known that the point P is in the fourth quadrant, and the distance to the X axis is , and the distance to the Y axis is 2, then the coordinate of the point P is _ _ _ _.

5. If it is known that the distance from the point P to the X axis is , and the distance to the Y axis is 2, then the coordinate of the point P is.

6.

7. Translate the point to the right by two units to get a point, and then translate the point up by three units to get a point, then the coordinates are;

8. In rectangular ABCD, a (-4,1), b (,1) and c (,3), then the coordinates of point D are;

9. The length of line segment AB is 3 and parallel to the X axis. If the coordinate of point A is (2, -5), the coordinate of point B is _ _ _ _.

2. Multiple choice questions:

1. The coordinates of two endpoints of line segment AB are A(1, 3) and B(2, 7). Then the relationship between line AB and line CD is ()

A. Parallel and equal B. Parallel but unequal C. Non-parallel but equal D. Non-parallel and unequal

3. Solution:

1. Known: as shown in figure,,, find the area of △.

2. Known:,, the point is on the axis.

(2) If, find the coordinates of points.

3. It is known that the coordinates of vertices of quadrilateral ABCD are A(-4, -2), B(4, -2), C (3,1), D (,3).

(1) Draw quadrilateral ABCD in a plane rectangular coordinate system;

(2) Find the area of the quadrilateral ABCD.

(3) If you subtract 2 from the abscissa of each vertex of the original quadrilateral ABCD and add 3 to the ordinate, what is the area of the graph?

4. It is known that:,,.

(1) Find the area of △;

(2) Set a point on the coordinate axis,

and the area of △ and △ is equal,

Find the coordinates of the point.

5. As shown in the figure, it is a schematic plan of a wild zoo. Establish an appropriate rectangular coordinate system, write down the coordinates of each point, and find the actual distance between the goldfish hall and the panda hall.

6. As shown in the figure, translate the coordinates. Get,

draw, and find out the coordinate change from △ABC.

Chapter VII Triangle

(1) Knowledge structure diagram of this chapter:

(2) Examples and exercises:

1. If an external angle of a triangle is smaller than its adjacent internal angle, Then this triangle is ()

A. acute triangle B. right triangle

C. obtuse triangle D. acute triangle or obtuse triangle

2. As shown in the figure, a pair of triangular rulers are spliced into a pattern, then ∠ AEB = _ _ _ _ _ _ _ _.

3. In △ABC, Then the value range of side C is _ _ _ _ _ _ _. < P > 4. If the ratio of three line segments is: < P > (1) 5: 2: 3 (2) 5: 1: 15 (3) 3: 4: 5 < P > (4) 3: 3: 5. .2b.3c.4d.5

5. The three sides of a triangle are 3, 8 and 1-2x respectively. The value range of x is ()

a. < x < 2b.-5 < x <-2c.-2 < x < 5d. x <-5 or x > 2

6. If the intersection points of heights on two sides of a triangle are outside the triangle, then the triangle is _ _ _ _ _ _ (2) the angular bisector AE of △ ABC;

8. given △ABC, find the high-speed line AD and CE of △ABC.

9. in △ABC, two bisectors BD and CE intersect at point o, ∠ BOC = 116, so the degree of ∠A is _ _ _ _ _ _.

1. it is known that BD and CE are the heights of △ABC. if one of the angles formed by the intersection of straight lines BD and CE is 5, ∠BAC is equal to _ _ _ _ _ _ _ _ _ _.

11. in △ABC, ∠ b-∠. Then the number of sides of this polygon is ()

a.5b.6c.7d.8

13. Each of a polygon.