O

A

B

C

D

E

Example 1 chart

Example 1 As shown in the figure, O is a point on the straight line AB, and the angle smaller than the right angle in the figure is [].

a，7 B，8 C，9 D， 10

At 8: 30am Beijing time, the angle between the hour hand and the minute hand on the clock (less than 1800) is [].

850 pounds 750 pounds

700 D、600 c

A

B

C

M

ordinary

Example 3 is shown in the figure. The line segment AB=a, C is a point on AB, M is the midpoint of AB, MC=b, and N is the midpoint of AC. How many line segments are there in the graph (1)? (2) Find the length of MN.

As the picture shows, there are four villages with ABCD on the plain. In order to solve the local water shortage problem, the government intends to invest in building a reservoir. Without considering other factors, please draw a picture to determine the location of point H of the reservoir so as to minimize the sum of the distances between it and the four villages.

C

D

A

B

Second, practice is improved.

1 questions

O

A

B

C

D

Solid foundation

1, as shown in the figure, the number of line segments in the figure is []

a、6 B、8 C、 10 D、 12

2. The following statement is correct []

A, the figure composed of two rays is called angle b, and the size of the angle has nothing to do with the length of the side.

C, ray OA and ray AO represent the same ray d, and one ray is a fillet.

3. If point C is the midpoint of line segment AB, then ① AB = 2aC; ②2BC = AB； ③AC = BC； (4) AC+BC = AB。 Of the above four formulas, the correct one is []

a， 1 b，2 c，3 d，4

Draw a straight line through A, B and C. Xiaoming said there were three, Xiaoying said there was one, and Xiaolin said there was either one or three. what do you think?

You're right.

It only takes two nails to nail a thin board to the wall.

6. After straightening the curved river, the length of the river is shortened because.

7.(37. 145) 0 = degrees, minutes and seconds; 98030' 18'' = degrees.

8. At 2: 30 pm, the angle between the hour hand and the minute hand in the clock is [].

a 900 B 1050 C 1200D 1350

9. Take three points A, B and C in turn on a straight line, so that AB=4㎝, BC=3㎝, and point O is the midpoint of line segment AC, then the length of line segment OB is [].

A, 2 inch b, 1.5 inch c, 0.5 inch d, 3.5 inch.

10, as shown in the figure, the following statement is true ()

(a) point a is on line BO;

Aboo

(b) Point A is on the thunder wave;

(c) Point A is on the extension line of line segment BO;

(d) Point A is on the reverse extension line of line segment BO.

a

b

1 1. Given line segments A and B, draw line segment A+B.

12. It is known that point C is the midpoint of line segment AB, point D is the midpoint of BC, and AB= 10㎝. Find the length of AD.

13 questions

A

B

C

D

Ability improvement

13, as shown in the figure, the number of angles in the figure is [].

a、5 B、6 C、7 D、8

14. If the line segment AB = 13 ㎝ and MA+MB= 17㎝, then

The following statement is incorrect []

Points a and m are on line AB.

15 questions

A

B

C

Point b and point m are on the straight line AB.

Points c and m are outside the line segment AB.

Points d and m may be on the straight line AB, or they may be on.

Outside the straight line AB

15, as shown in the figure, in the triangle ABC, BC < AB+AC, because.

16. Three intersecting lines have at least two intersections and at most one intersection.

17, there are four points on line A, point A, point B, point C and point D, so there is a line segment on line A. 。

18, it is known that the line segment AB = 5 ㎝, C is a point on the straight line AB, and if BC=2㎝, the length of the line segment AC is.

19, as shown in the figure, AB = 16 ㎝, C is the midpoint of BC, AC= 10㎝, D is the midpoint of AC, and E is the midpoint of BC. Find the length of line segment DE.

A

B

C

D

E

20. on the straight line l, take points a, b, c and d in the specified direction, so that AB: BC: CD = 2:

3: 4, if the distance from the midpoint M of AB to the midpoint N of CD is 15㎝, what is the length of AB?

Exploration and innovation

2 1. Observe the picture below and read the related text below:

Two straight lines intersect, and there are at most 1 intersections.

Three straight lines intersect, and there are at most three intersections.

Four straight lines intersect, and there are at most six intersections.

…

Guess: (1) How many intersections do five straight lines have at most? What about six straight lines?

(2) How many intersections do n straight lines have at most?

"Line, Angle" Basic Test (90 minutes) Name Courseware

I. True or false questions (2 points for each small question, *** 16 points).

1. After every two of the three points, * * * can draw three straight lines (). 2. The ray AP and the ray PA are the same ray ().

3. The line segment connecting two points is called the distance between these two points (). 4. Two straight lines intersect, and there is only one intersection point ().

5. A figure composed of two rays is called an angle (). 6. The side length of the angle determines the size of the angle. ()

7. Two complementary and equal angles are 45 (8). If two angles are complementary, one of them must be an obtuse angle ().

II. Fill in the blanks (65438+ 0 for each blank, ***28)

1. Draw a straight line on every two of the three points on the intersecting plane. At least _ _ _ lines can be drawn, and at most _ _ _ lines can be drawn.

2. As shown in the figure, there are four points C, D, E and F on the line segment AB, so * * in the figure has _ _ _ _ line segments.

3. The point C is on the straight line AB, and the line segment AB = 6 cm and BC = 4 cm, so the length of the line segment AC is _ _ _ _ _.

4. Extend the line segment AB to point C to make BC = AB, and then extend BA to point D to make AD = 2AB.

Then DC = _ AB = _ AC；; BD = _ _ _ _ _ _ AB = _ _ _ _ _ _ DC。

5.45 = _ _ _ _ _ Right angle = _ _ _ _ Flat angle = _ _ _ Fillet.

6. 18.26 =___ ___′___″; 12 36′ 18″=______ .

7. Only _ _ _ has a surplus angle, and its surplus angle is _ _ _ _.

8. As shown in figure ∠ AOC = ∠ COE = ∠ BOD = 90, then the angle ∠BOC equals _ _ _ _ _;

The complementary angle with ∠BOC is _ _ _ _, and the complementary angle with ∠BOC is _ _ _ _ _.

9.∠ A equals the remaining angles ∠b equals the remaining angles, then ∠ A+∠ B = _ _ _.

10. If the difference between two complementary angles is 35, the complementary angle of the larger angle is _ _ _ _.

1 1. When the clock is at 12, the angle formed by the hour hand and the minute hand is _ _ _ _.

12. Fill in the blanks with definitions and attributes:

(1) As shown in the figure below, ∫m is the midpoint of AB, ∴ am = MB = AB. ()

( 1) (3)

(2) As shown in the figure below, ∫OP is the bisector of ∠MON.

∴ ∠MOP=∠NOP= ∠MON。 ( )

(3) As shown above,

∵ Points A, B and C are on a straight line; ∴ ∠ABC is a right angle ()

(4) As shown in the figure below,

(2) (4)

∵ ∠ 1+∠2=90 ,∠3+∠2=90 ,∴ ∠ 1=∠3( )

Iii. Multiple choice questions (2 points for each small question, *** 16 points)

1. As shown in the figure, b, c and d are points on the ray AM, so there are … () rays in the figure.

(A)6 (B)5 (C)4(D) 1

2. In the following four groups of graphs (where AB is a straight line, CD is a ray, and MN is a line segment), which can intersect is ().

(A) (B) (C) (D)

3. As shown in the figure, from AB = CD, the relationship between AC and BD is ().

(a) AC > BD (b) AC < BD (c) AC = BD (d) cannot be determined.

4. As shown in the figure, m is the midpoint of the line segment AB, n is a point on the line segment AB, AB = 2A, NB = B, in the following statement.

The mistake is () (a) am = a (b) an = 2a-b (c) Mn = a-b.

(D)MN= a

5. The following statement is true ()

(a) the light rotates to form an angle; (b) Both sides of the angle can be measured.

(c) A straight line is a right angle. (d) Both sides of a right angle can be regarded as a straight line.

6. Among the following four graphs, the graphs that can correctly represent the same angle in three ways are ∞, ∠O and ∠AOB ().

(A) (B) (C) (D)

7. As shown in the figure, ∠AOB is a right angle, ∠ AOC = 40, and OD bisects ∠BOC, then ∠AOD is equal to () (a) 65 (b) 50 (c) 40 (d) 25.

8. The following statement is correct in ........................................ ().

(a) The complementary angle of an angle must be greater than this angle. (b) The complementary angle of an acute angle is an acute angle.

(c) The complementary angle of a right angle is a right angle. Acute and obtuse angles must be complementary.

Four. Calculation (4 points for each small question, *** 16 points)

1.37 28′+44 49′; 2. 108 18′-52 30″;

3.25 36′×4; 4.40 40′÷3.

Verb (abbreviation of verb) solving problems (8 points for each small question, * * * 24 points)

1. As shown in the figure, m is the midpoint of line segment AB, point C is on line segment AB, AC = 4 CM, N is the midpoint of AC, and Mn = 3 cm. Find the length of line segments CM and AB.

2. It is known that ∠a and ∠b are complementary angles, and the ratio of ∠b is larger than ∠ A 15, so we can find the complementary angle of ∠ A. 。

3.∠AOB is a right angle, OC is outside ∠ AOB, ∠AOC is equal to 46, OM bisects ∠AOC, and on bisecting ∠BOC, find the degree of ∠MON.