Name _ _ _ _ _ Student ID _ _ _ _ _ _ _ _

First, the intersection line, three-line octagon

1. The number of intersecting lines on the plane is _ _ _ _ _ _ _.

2. On the same plane, the positional relationship between the straight line and the straight line L is _ _ _ _ _ _

3. Two straight lines intersect, at most 1 intersection, three straight lines intersect, at most _ _ _ intersection, four straight lines intersect, at most _ _ _ _ _ intersection, and n straight lines intersect, at most _ _ _ _ _ _ _.

4. As shown below, O is a point on the straight line AB, ∠ COB = 26 30', then ∠1= _ _ _

5. As shown above, the straight lines AB and CD intersect at O, ∠ 1-∠ 2 = 85, ∠ AOC = _ _ _ _.

6. It is known that ∠AOB and ∠BOC are adjacent complementary angles, OD is the bisector of ∠AOB, OE is in ∠BOC, ∠BOE= ∠EOC, ∠ DOE = 72, and the degree of ∠EOC is found.

7. As shown in the figure below, ∠ 1 and ∠2 are _ _ _ _ _ _ _ 3 and ∠4 are _ _ _ _ _ _ formed by a straight line _ _ _ _ _ _ (please fill in "congruent angle", "inner angle" and ".

8. As shown in the above figure, there are _ _ _ angles that are inscribed with ∠, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

9. As shown in the above figure, there are _ _ _ angles that can form the same internal angle with ∞.

10. The relationship between a straight line and the other two parallel lines is ()

A. it must be parallel to two parallel lines.

It may be parallel or intersect with one of two parallel lines.

C. it must intersect with two parallel lines.

D. parallel to or intersecting with two parallel lines.

Second, the vertex angle, vertical line and their properties

1. If the straight line is b⊥a and c⊥a, then B _ _ C.

2. There are _ _ _ lines perpendicular to the known lines.

3. There is a highway MN due south of Village A, and the shortest route from Village A to the highway is through point A as AD⊥MN and point D, so the reason for this design is _ _ _ _ _ _ _ _ _ _ _ _ _ _; Village B is adjacent to Village A, and the shortest route between villagers in the two villages is the length of AB line, on the grounds that _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

4. As shown in the right figure, BC⊥AC, CB=8cm,

AC=6cm, AB= 10cm, then arrive at point B.

The distance from AC is _ _ _ _ _, and point A reaches BC.

The distance between a and b is _ _ _ _ _ _ _.

5. As shown in the figure below, if 2∠3=3∠ 1, ∠ 2 = _ _ _ _,

∠3=____ ,∠4=____ 。

5. As shown in the upper right figure, straight lines a⊥b, ∠ 2 = 40, ∠1= _ _ _ _ _

6. It is known that OA⊥OC is at point O, ∠AOB: ∠AOC=2:3, so the degree of ∠BOC is _ _ _ _ _ _ _ _.

7. As shown in the figure below, given OA⊥OC, OB⊥OD, and ∠AOD=3∠BOC, find the degree of ∠BOC.

8.OC divides ∠AOB into two parts, and the following two equations hold: ①∠AOC= right angle+∠ BOC; ;

②∠BOC= flat angle -∠AOC

Q: (1) What is the positional relationship between OA and OB?

(2) 2) Is OC the bisector of ∠AOB? And write the reasons for the judgment.

10. It is known that straight line AB and CD intersect at point O, ray OE⊥AB is at point O, ray OF⊥CD is at point O, and ∠ BOF = 25. Find the degree of ∠AOC and ∠EOD

Third, the nature of parallel lines.

1. If a person starts from point A, walks 60 northeast to point B, then starts from point B and walks to point C in southwest15, then ∠ABC is equal to ().

135

2. As shown in the figure below, the direction of point B measured from point A is _ _ _ _ _.

As shown in the upper right, a highway needs to go around the lake when it is built to the lake. It is known that the angle of the first circle is ∠A, and ∠ A = 120, the angle of the second circle is ∠B, and ∠ B = 150, and the first circle is.

120， 130， 140， 150

4. In the following figure, the one that can get ∠ 1=∠2 from AB//CD is ().

5. There are three points A, B and C on the same side of the straight line L. If the straight line passing through A and B is parallel to the straight line passing through B and C, the three points A, B and C are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

6. As shown in the left figure, if it is known that AB//CD, BE bisects ∠ABC, ∠ CDE = 160, then ∠ C = _ _ _ _ _

7. If AB//CD and FG share ∠EFD, ∠ 1 = 70, ∠ 2 = _ _ _

Fourth, the determination of parallel lines

1. As shown in figure 1, write a suitable condition to make AD//BC. This condition is _ _ _ _ _ _.

2. As shown in Figure 2, the condition that AB//CD cannot be determined is ().

A.∠DAC =∠ACB b∠BAC =∠DCA

C.∠ABC+∠DCB = 180d .∠BAD+∠CDA = 180

3. As shown in Figure 3, given that ∠ 1+∠ 2 = 180, ∠ 1=∠3, is EF parallel to GH? Why?

4. As shown in the figure, straight lines AB and CD are cut by straight line EF. If ∠ 1=∠2, ∠CNF=∠BME, then AB//CD, MP//NQ, please explain the reason. (Variant: If MP and NQ share ∠BMF and ∠DNF, respectively, MP//NQ is verified)

5. As shown below, line A and line B are cut by line C, and the following four conditions are given: ① ∠1= ∠ 5; ②∠2+∠7= 180 ; ③∠2+∠3= 180 ; ④∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠87

6. If there is no auxiliary line in the upper right picture, write one that can judge EB//AC _ _ _ _ _

Fifth, the judgment and nature of parallel lines are comprehensively investigated.

1. An expressway turns twice, and the original direction is the same. If the first right turn is 60, the second turn is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

2. If AB//CD, OE shares ∠BOC, OE⊥OF and ∠ DOF = 29, then ∠ B = _ _ _ _

3. As shown in the upper right figure, points E, F, D and G are all on the edge of △ABC, EF//AD, ∠ 1=∠2, ∠ BAC = 55, and find the degree of ∠AGD.

4. DF//AC is known, ∠C=∠D, and verification: BD//CE.

5. As shown in the figure, place a pair of triangular plates so that point A is on DE, and the degree of BC//DE and AFC is _ _ _ _ _ _ _.

6. As shown in the figure, if AB//CD is known, the equivalent relationship between,, and is _ _ _ _ _ _ _ _.

7. As shown in the figure below, AB//CD, BF bisection ∠ABE, DF bisection ∠CDE, ∠ Bed = 75, then ∠BFD = _ _ _ _ _ _ _

8. As shown in the upper right, it is known that ∠ ABC = 90, ∠ 1=∠2, ∠DCA=∠CAB. Try to explain the CD split ∠ACE.

Six, proposition and its structure

1. Write the following proposition in the form of "If … Then …" to judge whether it is true or not.

(1) The complementary angles of the same angle are equal.

(2) The same angle is equal

(3) When the sum of two angles is equal to a right angle, the two angles are complementary.

(4) Two parallel lines are cut by a third straight line, and the internal dislocation angles are equal.

(5) Equivalent substitution

(6) The circumference of a circle is 2π r. 。

2. There are the following statements: ① Draw the bisector of ∠AOB; 2 right angles are equal; (3) Are the internal angles on the same side complementary? ④ Determine a straight line at two points; Among them, _ _ _ _ _ _ _ _ _

3. The included angle of the bisector of adjacent complementary angles is a right angle, and this proposition is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Seven. Translation, drawing and related calculations

1. Translate the line segment with a length of 8cm to the southeast by 6cm, and the length of the line segment obtained is _ _ _ _ _ _ _ _.

2. Move an eraser on the blackboard 10cm. In the following statement, the wrong one is ().

A. All four vertices have been translated by10cm.

B. The position after translation and before translation has changed, but the occupied area has not changed.

C. the connecting line of the corresponding point is a parallel line segment.

D the horizontal translation distance is 10cm.

3. If a 6cm long line segment AB is translated to the left by 4cm to get PQ, PQ = _ _ _ _ _ _ _ AP = _ _ _ _ _ _

4. Graphics are translated from one location to another. In the following statement, the wrong one is ().

A. Any point on the diagram moves in the same direction.

The moving distance of any point on the graph is equal.

C. there may also be fixed points on the diagram.

D the connecting lines of any pair of corresponding points on the graph are equal in length.

5. As shown in Figure ①, there are two paths on the rectangular lawn, length B and width A, both C, which are perpendicular to each other. In order to find the lawn area, Xiao Ming made the transformation as shown in Figure ②, so the lawn area can be expressed as _ _ _ _ _ _ _ _.

6. Translate △ABC so that point A faces 60 northeast and the distance on the map is 2cm.

7. It is known that ∠BAC in obtuse angle △ABC is obtuse.

(1) Draw a vertical line from point C to AB;

(2) Draw the vertical line of BC through point A;

(3) Measure the distance from point B to AC.

8. Site selection for bridge construction: As shown in the figure, A and B are on both sides of a river, and now a bridge is to be built on the river. Where can I build a bridge with the shortest path AMNB from A to B? Assuming that the two banks of the river are parallel straight lines, the bridge should be perpendicular to the river. )