I. Choice (3 points for each small question, ***27 points)

1. In the same plane, the positional relationship between two straight lines may be ().

A, intersection or parallel b, intersection or vertical c, parallel or vertical d, uncertainty

2. As shown in the figure, ∠ 1 and ∠2 are graphs with opposite vertex angles ().

A B C D

3. The following statement is true ()

(1) vertex angles are equal; (2) Equal angle is the opposite angle; (3) If two angles are not equal, they must not be antipodal angles; (4) If two angles are not opposite, they are not equal.

1。

4. Point P leads to the vertical line where line segment AB is located, and the correct one is ().

A B C D

5. AB, CD, CD intersect at O, OE⊥CD intersect at O, ∠ AOC = 36,

Then ∠BOE= ().

(A) 36 (B)64

144 (D)54

6. As shown in figure 1, if three straight lines AB, CD and EF intersect at point O, then ∠AOE+∠ Dobby +∠COF is equal to ().

150 b . 180 c . 2 10d . 120

7. As shown in figure 1, the following statement is wrong ().

A, ∠A and ∠C are ipsilateral internal angles B, ∠ 1 and ∠3 are congruent angles.

C, ∠2 and ∠3 are internal angles D, ∠3 and ∠B are internal angles on the same side.

8. As shown in Figure 2, ∠ 1 = 20, AO⊥CO, and points B, O and D are on the same straight line, then the degree of ∠2 is ().

a、70 B、20 C、 1 10 D、 160

9. In a 5×5 grid paper, the position of the graphic n in Figure 3- 1 after translation is shown in Figure 3-2, so the correct translation below is ().

A. Move 1 grid down first, and then move 1 grid left; B. First move down 1 grid, and then move 2 grids to the left.

C. First move down 2 squares, and then move to the left 1 square; D. First move down 2 squares, then move left 2 squares.

Fill in the blanks (3 points for each small question, ***27 points)

1. As shown in the figure, three straight lines AB, CD and EF intersect at point O, and the antipodal angle ∠ AOC is ∠COF.

The diagonal of is

2. A little _ _ _ _ _ _ is perpendicular to the known straight line.

3._ _ _, these two straight lines are perpendicular to each other, and one of them is straight.

It is called another straight line _ _ _ _, and their intersection is called _ _ _ _.

4. As shown in Figure 4, if ∠ 1 = 25, ∠ 2 = _ _ _ _, ∠ 3 = _ _ _ _, ∠ 4 = _ _ _ _.

5. As shown in Figure 6, it is known that straight lines AB and CD intersect at O, OA bisects ∠ EOC, ∠ EOC = 70, then ∠ BOD = _ _ _ _ _.

6. As shown in Figure 9, straight lines AB and CD intersect at point O, and it is known that ∠ AOC = 70, OE divides ∠BOD into two parts, ∠BOE:∠EOD=2:3, then ∠ EOD = _ _ _ _ _ _ _

7. ∠AOB shown in the figure, ∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠873

8.( 1) ∠ 2 and ∠4 are straight lines and are cut by straight lines _ _ _.

(2) ∠ 1 and ∠3 are straight lines and are cut by straight lines.

9. As shown in figure OC⊥AB at point O ∠ 1=∠2, then the complementary angle in the figure is right.

Three. Answer questions (1 and 2 questions with 7 points, 3-6 questions with 8 points, and * * * questions with 46 points).

1. It is known that line A and line B intersect, ∠ 1 = 40.

Find the degrees of ∠2, ∠3 and ∠4?

2. As shown in the figure, three straight lines AB, CD and EF intersect at point O. If ∠1= 40 and ∠ 2 = 75, how many degrees is ∠3?

3. As shown in the figure, the straight line DE. BC is cut by straight line AB.

What are the angles of (1) ∠ 1 and ∠ 2, ∠ 1 and ∠ 3, ∠ 1 and ∠ 4?

(2) If ∠ 1 =∠ 4, is ∠ 1 equal to ∠ 2? Are ∠ 1 and ∠ 3 complementary?

4. As shown in the figure, it is known that straight line AB intersects with CD at point O, ∠DOE is complementary to ∠BOD, ∠ DOE = 40, and the degree of ∠AOC is found.

5.AB, CD and EF are all straight lines, where ∠3=∠4, and the simple reason for trial ∠ 1=∠2.

6. As shown in the figure, straight lines A, B and C intersect in pairs, ∠ 1 = 2 ∠ 3, ∠ 2 = 65, and the number of times to find ∠4.

Answer: One. 1.A 2。 C 3。 B 4。 C 5。 D 6。 B 7。 B 8。 C 9。 C

2. 1.∠BOD∠EOD 2。 There is only one straight line 3. One of the four angles formed by the intersection of two straight lines is

90, vertical, vertical foot 4.155,25, 155 5.35 6.42 7.2 1 8. (1) BC, EF, ED, congruence angle (2) AB, DE, BC, and internal dislocation angle (9. 4).

Three. 1. Solution: ∠ 3 = ∠ 1 = 40 (equal to the vertex angle)

∠2= 180 -∠ 1= 180 -40 = 140

(Definition of Complementary Angle)

∠ 4 =∠ 2 = 140 (equal to the vertex angle)

2. Solution: ∫≈ 1+∠AOF+∠2 = 180 (definition of right angle).

∴∠AOF= 180 -(∠ 1+∠2)

∵∠ 1=40 , ∠2=75

∴∠aof= 180- 1 15 = 65

∴∠3 =∞∠aof = 65° (equal to the vertex angle)

(1) ∠ 1 and ∠ 2 are internal angles.

∠ 1 and∠ 3 are ipsilateral internal angles.

∠ 1 and∠ 4 are isosceles angles.

(2)∫∠ 1 =∠4 (known)

∠ 2= ∠ 4 (equal to the vertex angle)

∴ ∠ 1=∠ 2 (equivalent substitution)

∵∠ 4 +∠ 3 = 180 (definition of adjacent complementary angles)

∠ 1 =∠ 4 (known)

∴∠ 1.+∠ 3 = 180 (equivalent substitution)

4. Solution: ∫∠DOE and ∠BOD are complementary (known).

∴∠ DOE+∠ BOD = 90 (meaning of complementarity)

∴ ∠BOD=90 -∠DOE= 90 -40 =50

∫∠DOB and ∝∞∠AOC are diagonally known.

∴∠AOC =∠DOB (equal to vertex angle)

∴∠AOC=50

5. Solution: ∫∠1+∠ 3 =180 ∠ 2+∠ 4 =180 (definition of adjacent complementary angle).

∴∠ 1+∠3=∠2+∠4

∠3=∠4

∴∠ 1=∠2

6. Solution: ∫∠2 = 65∴∠∠ 1 =∠2 = 65 (the opposite angle is equal) and ∣∣∣ 2 = 8.

∴∠ 4 =∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠

Volume II

1. If four different straight lines intersect at one point, how many pairs of vertex angles are there in the graph * * *? What happens when n different straight lines intersect at one point? (6 points)

2. Given that point O is a point on straight line AB, OC and OD are two rays, and ∠AOC=∠BOD, then ∠AOC and ∠BOD are diagonal? Why? (6 points)

3. As shown in Figures A and B, there are two wheat fields, P is the reservoir, and there is a canal between A and B. Now it is necessary to lead the water in the reservoir to A and B to irrigate the wheat. How do you think building canals can save time and materials? Please state your design scheme and explain the reasons. (8 points)

Answer: 1. Answer: Four different straight lines intersect at one point. In the picture, * * has an antipodal angle of 12 (except boxers), and n different straight lines intersect at one point. In the picture, * * * has (n2-n) antipodal angle (except boxers).

Answer: ∠AOC and ∠BOD are not necessarily at right angles. As shown in figure 1, when rays oc and OD are located on one side of straight line AB, they are not at right angles; As shown in fig. 2, when the rays OC and OD are located on both sides of the straight line AB, they are diagonal.

3. Draw a vertical line from point P to the line where A and B are located, and the vertical foot is D. It is economical and time-saving to repair the waterway along the vertical line PD.

Reason: The vertical line is the shortest. (Figure omitted)