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A case study of eighth grade mathematics counseling in Beijing Normal University
The fourth chapter quadrilateral natural exploration unit test paper

Class: Seat: Name: Grade: _ _ _ _ _ _

1. Fill in carefully (the answer is written in the designated horizontal line of this test paper, with 3 points for each small question and 30 points for * * *).

1, as shown in figure 1, in □ABCD, ∠ BAC = 34, ∠ ACB = 26, ∠ DAC =; ∠ACD =; ∠B = _ _ _ _ _; ∠D=______ .

2. Parallelograms are equal; Equality; Divide each other equally.

3. As shown in Figure 2, in □ABCD, it is known that △ ADO = 90 and OA = 6cm;; OB=3cm, then AD = _ _ _ cm, AD = _ _ _ cm.

4. As shown in Figure 3, quadrilateral ABCD, AC and BD intersect at point O. If OA=OC, the following conditions need to be added to make quadrilateral ABCD a parallelogram.

5. As shown in Figure 4, □ABCD, where E and F are the midpoints of AB side and DC side respectively, there is a parallelogram in the figure.

6. If the diagonal length of a diamond is 6 and 8 respectively, its circumference is and its area is.

7. As shown in Figure 5, in the rectangular ABCD, the diagonal AC and BD intersect at point O, and AB=OA=2cm, then the length of BD is _ _ ________cm, and the length of BC is _ _ _ _ _ _ _ _ _ cm.

8. If the sum of the internal angles of a regular N-polygon is equal to 1080, then the number of sides of this regular N-polygon is n = _ _ _ _.

9. As shown in Figure 6, in the trapezoidal ABCD, AB‖CD, AD=BC=DC, ∠ A = 45,

DE⊥AB is in E, and DE= 1, then the circumference of trapezoidal ABCD is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

10, the corresponding points of the central symmetric figure pass through and are equally divided.

Second, choose one item carefully, and fill in the answer letter in brackets (3 points for each small question, 24 points for * * *):

1 1. The number of the following beautiful patterns that are both axisymmetric and centrally symmetric is ()

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

12, the graph that can't spread intensively is ()

A, equilateral triangle b, equilateral quadrilateral c, equilateral pentagon d, equilateral hexagon

13, the following proposition, the correct proposition is ()

A, two quadrangles with equal diagonals are parallelograms;

B, two quadrangles with equal diagonal lines and perpendicular to each other are rectangles;

C, a quadrilateral with two diagonal lines bisecting each other vertically is a diamond;

D. A quadrilateral with two diagonal lines bisected and equal is a square.

14, the following conditions cannot determine that the quadrilateral ABCD is a parallelogram ().

a、AB=CD,AD‖BC B、AB=CD,AB‖CD

c、AB‖CD、AD‖BC D、AB=CD、AD=BC

15, Xiao Ming makes a quadrilateral kite with two bamboo sticks of equal length, then the shape of the kite must be

() A, rectangle B, square C, isosceles trapezoid D, uncertain

16, the side length of the diamond is 5, one diagonal length is 8, and the other diagonal length is ()

a、4 B、6 C、8 D、 10

17. About quadrilateral ABCD: ① Two groups of opposite sides are parallel respectively; ② The two groups of opposite sides are equal respectively; ③ The angles of the two groups are equal; ④ diagonal AC and BD are equal; In the above four conditions, it can be judged that the quadrilateral ABCD is a parallelogram ()

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

18, if the diagonal length of a square is 2, then the area of the square is ().

a、4 B、2 C、D、

Iii. Answer the following questions (***46 points)

19, (8 points) As shown in the figure, quadrilateral ABCD is parallelogram AD= 12, AB= 13, BD⊥AD, and find the length of BC, CD and OB.

20.(8 points) As shown in the figure, in the parallelogram ABCD, AE⊥BD and CF⊥BD have vertical feet of E and F respectively.

(1) Write each pair of triangles that you think are congruent;

(2) Choose any pair of (1) to prove it.

2 1, (8 points) in □ABCD, e and f are on DC and AB respectively, DE=BF, is quadrilateral AFCE a parallelogram? Tell me your reasons.

22.( 10) As shown in the figure, in □ABCD, e and f are points on BC and AD respectively, and AE‖CF, is AE equal to CF? Explain why.

23.( 12 minute) The diagonal of the rectangular ABCD intersects at point O, DE‖AC, CE‖DB, and DE and CE intersect at E, so the quadrilateral DOCE is a diamond. Please write the explanation process.

Congratulations, you finally finished the exam!

Please check it again carefully to see if there are any missing questions and wrong questions. Be careful!

answer

1. 1,,.

2, opposite, diagonally opposite, diagonally opposite. 3、 。 4. Omit. 5、4。 6、20,24。

7、4, 。 8、8。 9、 , 。 10, center of symmetry.

Ii. 1 1, C. 12, C. 13, C. 14, A. 15, D. 16, B.

3. 19, solution 20, solution; 、

2 1, which proves that:

22. Proof: 23 Proof:

First unit

1. How often do you exercise?

→ How long+auxiliary verb do(does or did)+ subject+doing something. The interrogative word how often is asked, where the auxiliary verb do(does or did) helps to form a question.

Daily/weekly/twice a month/three times a month/three or four times a month.

2. What do you usually do on weekends?

The first do is an auxiliary verb, which plays an interrogative role in this help; The second do is a notional verb. I usually play football.

3. What is your favorite program? This is the animal world.

4. What do the students of Green High School do?

The first do is an auxiliary verb, which plays an interrogative role in this help; The second do is a notional verb.

As for homework, most students do homework every day.

About ... means "as for; About "is often used as an adverbial at the beginning of a sentence, followed by a noun, pronoun or verb in -ing. For example:

As for him, I never want to see him here. As for him, I never want to see him here.

As for this story, you'd better not believe it. You'd better not believe that story.

6. The result of "watching TV" is very interesting.

7. Mom wants me to get up at 6 o'clock and play table tennis with her.

Want to do sth. It means "want to do something"; Want someone. Do sth. I hope someone will do something, for example:

Do you want to go to the movies with me? Do you want to go to the movies with me?

The teacher doesn't want us to eat hamburgers. The teacher doesn't want us to eat hamburgers.

8. She said it was good for my health.

Beneficial to ... means "beneficial to ...". Its antonym is: harmful to ... (here for is a preposition followed by a noun, pronoun or gerund) For example:

Reading more books is good for us. Reading more books is good for us.

Reading in bed is harmful to your eyes. Reading in bed is harmful to your eyes.

9. How many hours do you sleep every night?

10. I exercise every day, usually when I come home from school.

1 1. I have a good eating habit. Here pretty is equivalent to very.

12. I try to eat more vegetables, usually ten to eleven times a week. Try to do sth. It means "trying to do something" and does not include whether it is successful/trying to do something. Try to do something (in some way). You'd better try to do this experiment in another way. You'd better try to do this experiment in another way.

13. My healthy lifestyle helps me get good grades. Help sb. Do sth. Help sb to do sth.

14. Good food and exercise help me study better. Help sb. Do sth. Help sb to do sth. /here better is the comparative degree of well, not the comparative degree of good.

15. Is her lifestyle the same as yours or different? Is her lifestyle the same as yours or different from yours? Be the same as/different from ...

16. I feel a little unhealthy. Species = a little/a meaning "a kind".

17. What sports do you play?

18. Many vegetables help you keep healthy. keep fit

19. You must eat as little meat as possible. Try to do sth. It means "try your best to do something" and does not include the meaning of success or failure. /less is the comparative of little.

20. That sounds interesting. This is a simple sentence with the structure of "subject+copulative verb+predicate". Words such as sound (sound), look (appearance), smell (smell), taste (taste), feel (seem), grow (change) and get (change) can be used as copula in English, followed by adjectives as predicates. For example:

It tastes good. It tastes good.

This music sounds sweet. This music sounds good.

The smoke is getting heavier and heavier. The smoke is getting thicker and thicker.

Second unit

1. What happened? What's the matter with you? With is a preposition followed by a noun, pronoun or gerund. Personal pronouns must use the objective case.

I have a cold/backache/stomachache.

You should lie down and rest/drink hot tea with honey/see a dentist/doctor.

I'm not feeling well. Good here refers to physical condition and cannot be replaced by good.

4. When did it start? About two days ago.

5.that's too bad.

I hope you get well soon. Here better is the comparative of well.

Traditional Chinese medicine believes that we need a balance between yin and yang to be healthy. Here, health is an infinitive verb phrase used as an adverbial of purpose.

8. May your yin be too heavy. Too many are followed by uncountable nouns and too many are followed by plural countable nouns.

9. It is easy to have a healthy lifestyle, and a balanced diet is very important. It is easy to do sth. It's important to do sth.

10. Everyone is tired sometimes. Here get is a connecting verb, and tired is an adjective as a predication, which belongs to the system structure.

1 1. A throw like this will give you a fear. Give it to sb. Something. = Give sth. To sb. Give sb sth.

12. Take it easy. This is unhealthy. Here get is a connecting verb and stress is a predication.

13. I have a toothbrush. I need to see a dentist. → Need means "need". When it is a notional verb, it is followed by an infinitive, and the negative form is Don' t/ don't need/don't need (to do sth. ); As a modal verb, it can only be used in negative sentences or questions. The negative form is not having to do something. ), and there are no other morphological changes except the past tense.

14. Eat a balanced diet to keep healthy. Keeping healthy is an infinitive verb phrase used as an adverbial of purpose.

15. I don't feel very good now. Now = now

Third unit

1. What are you going to do on vacation? I'm looking after my sister.

Where are you going to spend your holiday? Italy.

This is a special usage of the present continuous tense, indicating that something planned or arranged has not been done yet.

2. Who are you going with? I'm going with my parents. With my parents is a prepositional phrase, which is used as an accompanying adverbial here to modify the predicate verb are going.

3. When will you go? I intend to go on Monday.

4. What are you doing there? I am going hiking in the mountains.

5. How long will you stay? Just four days. I don't like being away for too long. The interrogative word hwo long is a question about the length of time or things, and here is a question about the length of time.

6. Have a good time. = Enjoy yourself. Have a good time.

7. Show me your photos when we go back to school. Show it to sb. Something. Show sth. To sb. Show it to sb.

8. I'm going to Hawaii for my holiday. For vacation is a prepositional phrase, which is used here as an adverbial of purpose to modify a predicate verb.

9. How is it there? Here like is a preposition, not a verb.

10. Can I ask you some questions about your holiday plan? Ask someone. Something.

1 1. The famous French singer Ben Lambert will take a long vacation this summer. → vacation

12. He considered going to Greece or Spain, but decided to go to Canada. Think about/decide here about and on are prepositions.

13. "I always spend my holidays in Europe," he said. "I want to do something different this time." → (1). Want to do something. (2) Modifying the attribute of indefinite pronouns (something, nothing, anything, etc.). ) often placed behind indefinite pronouns.

14. He plans to have a very relaxing holiday. Plan to do sth.

15. I plan to spend some time in the beautiful countryside.

16. I just finished making the last movie. Finish sth.

17. I heard that Thailand is a good place for sightseeing. It is an infinitive verb phrase, which is used as the postattribute of a good place.

18. She will go to Hong Kong on Tuesday. Leave a to b and a to B.

19. I want to ask you about visiting China. Visiting China is a verb infinitive phrase, which is used as a postattribute of place.

20. I plan to spend my holiday in Italy this weekend. To Italy is an infinitive verb phrase, which is used as the postattribute of my holiday.

2 1. What should tourists bring? Together with them are prepositional phrases, which are used as accompanying adverbials to modify the predicate verb take.

22. Where did you leave? Leave a place (note: from is a preposition)

Fourth unit

1. How do you go to school? The interrogative word how is the way to ask here.

I ride a bike/walk/take the subway. Ride a bike/bike/bus/train/subway/taxi/plane/plane/ship/boat. Walk.

How do I get there? Because there is an adverb, you can't say don't worry when you get there. Let me see your map. Okay, first …, next … and then …

2. How long will it take? The interrogative word hwo long is a question about time or the length of things.

It takes about 25 minutes to walk, and the bus 10 minutes.

How long does it take you from home to school?

It takes twenty-five minutes. Take sb. Time to do sth. Spend sb.' s time ... doing sth.

3. Lin Fei's home is about100km from school.

How far is it from your home to school? It's three miles.

How far do you live from school? I live 0/0 miles from the school/kloc.

How far is the interrogative word? This is a question of distance.

In other parts of the world, the situation is different.

6. In China, it depends on where you are. → depends on. decision

7. That must be much more interesting than taking a bus.

8. In North America, not all students go to school by bus. Not all is partial negation, which means not all; Not all of them.

9. The rest of the world is different from the United States.

10. A few students take the subway. → quantity = many

1 1. What do you think of the traffic in your town? Have a certain opinion of ... ...

12. When it rains, I take a taxi.

13. I have a map, but it is in Chinese.

14. If you have any questions, you can ask the police.

Fifth unit

1. Can you come to my party?

Sure, I'd love to. /Sorry, I can't. I must help my parents.

Can you play tennis with me?

The modal verb can plays a role in soliciting opinions from the other side here.

I spent too much time at home this weekend. Too many uncountable nouns followed; Plural number of countable nouns

That's too bad.

Maybe next time.

5. Thank you for your concern. Used as a preposition followed by a noun, pronoun or gerund.

6. Come and play. /Come and join us.

7. On Wednesday, I will play tennis with the school team.

I have to study for the science exam on Thursday. Have to emphasize the objective reasons; And subjective reasons must be emphasized.

9. Please keep quiet! I am studying hard. Try to do sth. It means "try your best to do something" and does not include the meaning of success or failure.

10. Do you want to come to my birthday party? Want to do sth. It means "want to do something"

1 1. Li Lei will go fishing with grandpa all day. All day.

12. Can you come to my house?

13. I'm free until 22 o'clock.

Sixth unit

I am more outgoing than my sister. → subject+verb+adjective comparative degree +than+ comparison object.

As you can see, we look the same in some aspects, and we look different in some aspects.

In any case, we all like to attend parties. Enjoy doing sth. Enjoy doing sth.

Liu Li has more than one sister. More than that.

Liu Li and Liu Ying have something in common. → Common (group) * * * same; pooling

Liu Ying is not as good at sports as her sister. Like ... and ... (among them, the adjective between as ... must use the original level); Its negative form is: not as(so) … as.

7. Liu Ying speaks more than Liu Li. Here is more the comparative degree of much than many.

8. Both girls attend many parties. Many = many many.

9. My friends are the same as me. Same as/different from … different from ….

10. I think good friends can make me laugh. Make sb. Do sth. Let someone do something.

1 1. For me, good friends like to do the same things with me. Enjoy doing sth.

12. That's not very important to me …

13. What's your opinion?

14. Should friends be different or the same? Same is often preceded by the definite article the.

15. I like having friends like me. /I like having friends who are different from me. Enjoy doing sth. Like is a verb meaning "like"; And like in are like me is a preposition, which means "like". Pay attention to the distinction between parts of speech.

16. I am quieter than most children in my class.

17. We all like to do the same thing. Enjoy doing sth. Enjoy doing sth.

18. Who do you think should get the job, Ruth or Ross?

19. You must be good at getting along with children/like telling jokes. Get along well with sb. Be kind to sb. Get along well with [somebody]/enjoy doing [something].

He kept talking. Stop doing sth. It means "stop what you are doing" and is the object of stop in the sentence. When the teacher came in, the students stopped joking. The teacher came in and the students stopped joking. /stop to do sth. It means "stop (what you are doing) to do something" and the infinitive phrase to do something. Used as the adverbial of purpose of the verb stop in a sentence. He stopped to write a letter to her. He stopped what he was doing and wrote to her.

2 1. He always helps others.

22. She likes to stay at home and read. Enjoy doing sth. Enjoy doing sth. /Stay at home.

Review unit 1-6

1. You can make cheese with milk, and you can also drink it. The infinitive phrase "making cheese" is used here as an adverbial to modify "using milk".

2. a part of your body begins with a. → begin with … (note: with is a preposition)

The antonym of "short" is "long" or "high".

The neck is between your head and your body. → Between ... and ...

Carrots, onions and peppers are all vegetables. → All is used for three or more people; Use both. At the same time, we should pay attention to their position in the sentence, that is, they are behind the connecting verb (be) and auxiliary verbs (be, will, shall, should, etc.). ) and modal verbs (can, may, must, have to, etc. ); Before other verbs.

6. I like reading books in my spare time. Enjoy doing sth. Enjoy doing sth. In my spare time.

7. I feel terrible, doctor. Here, feel is a connecting verb, terrible is an adjective as a predicate, and feel terrible is a system structure as a compound predicate.

I usually relax in my swimming pool.

9. I am very excited to spend my holiday in China! Be excited about doing sth. Be excited about doing sth.

10. Who is stronger, Gao Yan or thomas lee?

Baidu won't let you type too many words, so that's it-convex.