1: A point outside the straight line is called the distance from the point to the straight line.

2. Axiom of parallel lines.

3. Conditions of parallel lines:

;

.

4. The essence of parallel lines:

;

.

The sum of the external angles of the 5:n polygon is; The sum of internal angles is.

6. An N-polygon starting from a vertex can be a diagonal line, which divides the polygon into two parts.

Triangle.

7. From one of the binary linear equations,

This method is called substitution method for short.

8. Coefficients of the same unknown quantity in two equations

This method is called addition and subtraction for short.

9: For 2x-y=3, we have a formula to indicate that y is:.

10: For four pieces of 10cm, 7cm, 5cm and 3cm, three pieces are selected to form a triangle, and the circumference of the triangle is.

Second, the solution and application

1, as shown in Figure ①, is the rest of the trapezoidal iron sheet. What are the other two corners of the trapezoid? (4 points)

2. As shown in Figure ②, a//b, c and d are cutting lines, 1=80, 5=70. What are the degrees of 2, 3 and 4 respectively? Why? (6 points)

3. In the plane rectangular coordinate system, mark the following points:

Point A is on the Y axis, above the origin, and 2 unit lengths away from the origin;

Point B is on the X axis, on the right side of the origin, and is 1 unit length away from the origin;

Point C is on the X axis and on the right side of the Y axis, and the distance between every two coordinate axes is 2 unit lengths;

Point D is on the X axis, located on the right side of the origin, and 3 unit lengths away from the origin;

Point E is located above the X axis and to the right of the Y axis, 2 unit lengths away from the X axis and 4 unit lengths away from the Y axis.

Connect these points in turn. What do you think it looks like? (8 points)

4. As shown in Figure ③, in the triangle AOB, the coordinates of point A and point B are (2,4) and (6,2) respectively. Find the area of triangle AOB (hint: the area of triangle AOB can be regarded as the area of a rectangle minus the area of some small triangles). (8 points)

5. Calculate the degree of each internal angle of regular pentagon and regular decagon. (5 points)

6. The sum of the internal angles of the polygon is equal to 1260. How many polygons does it have? (5 points)

7. As shown in Figure 4, 1 = 2, 3= 4, A= 100, find the value of x .. (6 points)

8. Solve the following equation as required (***8 points)

( 1) x+2y=9 (2) 2x-y=5

3x-2y=- 1 3x+4y=2

Three, the application of binary linear equations (7 points per question, ***35 points)

1. According to market research, the sales ratio of a disinfectant in large bottles (500g) and small bottles (250g) is 2: 5. A factory produces 22.5 tons of this disinfectant every day. How many bottles should these disinfectants be divided into large bottles and small bottles?

2. Two big harvesters and five small harvesters work for 2 hours to harvest wheat. 6 hectares, 3 big harvesters and 2 small harvesters harvest 8 hectares of wheat in 5 hours. 1 hour 1 NTU harvester and 1 small harvester harvest how many hectares of wheat?

3. The route from city A to city B is 1200km long. It takes 2 hours and 30 minutes for the plane to fly from A to B, and 3 hours and 20 minutes to fly from B to A against the wind. Find the average speed and wind speed of the plane.

4. Make tin cans with tin foil. Each tinplate can be made into 25 boxes or 40 boxes. A box body and two box bottoms form a set of boxes. At present, there are 36 sheets of iron. How many sheets are used to make the box, and how many sheets can make the box and the bottom just match?

5. It is necessary to use 30% and 75% of seed preservatives and 50% of antiperspirant to prepare 18kg preservative. How much do I need to take each of the two potions?