a) Ta có: \(\widehat{A_1}+\widehat{B_1}=90^o\) (\(\Delta ABH\) vuông tại H) (1)
lại có: \(\widehat{A_1}+\widehat{A_2}=90^o\) (\(\Delta ABC\) vuông tại A) (2)
Từ (1) và (2) \(\Rightarrow\) \(\widehat{A_2}=\widehat{B_1}\) (= \(\widehat{A_1}\))
\(\Delta ABH\) và \(\Delta CAH\) có:
\(\widehat{A_2}=\widehat{B_1}\) (cmt)
\(\widehat{H}\) chung
Vậy \(\Delta ABH\) đồng dạng với \(\Delta CAH\).

b) Áp dụng định lý Py-ta-go vào tam giác vuông AHB, ta có:
\(BH^2=AB^2-AH^2\)
\(\Leftrightarrow BH=\sqrt{15^2-12^2}\)
\(\Leftrightarrow BH\) = 9 (cm)
Ta có: \(\Delta ABH\) đồng dạng với \(\Delta CAH\)
\(\Rightarrow\) \(\left\{{}\begin{matrix}\dfrac{AH}{CH}=\dfrac{BH}{AH}\Leftrightarrow\dfrac{12}{CH}=\dfrac{9}{12}\Leftrightarrow CH=16\left(cm\right)\\\dfrac{AB}{AC}=\dfrac{BH}{AH}\Leftrightarrow\dfrac{15}{AC}=\dfrac{9}{12}\Leftrightarrow AC=20\left(cm\right)\end{matrix}\right.\)
Vậy BH = 9 (cm)
CH = 16 (cm)
AC = 20 (cm)

c) Ta có: \(\dfrac{CE}{AC}=\dfrac{CF}{CH}\left(\dfrac{5}{20}=\dfrac{4}{16}=\dfrac{1}{4}\right)\)
\(\Rightarrow\) EF // AH, mà AH \(\perp\) BC
\(\Rightarrow\) EF \(\perp\) BC
\(\Rightarrow\) \(\Delta CEF\) vuông tại F.

d) \(\Delta CEF\) và \(\Delta CBA\) có:
\(\widehat{A}=\widehat{F}\left(=90^o\right)\)
\(\widehat{C}\) chung
Vậy \(\Delta CEF\) đồng dạng với \(\Delta CBA\)
\(\Rightarrow\) \(\dfrac{CE}{CB}=\dfrac{CF}{CA}\)
\(\Rightarrow\) CE . CA = CF . CB (đpcm)

Từ sau khi ăn Tết Nguyên Đán, một bộ phận học sinh trường THCS A không còn tuân thủ nội quy nhà trường. Viết một bài văn nghị luận nêu quan điểm của em về vấn đề trên.

II. Change these sentences into the passive voice.

1. Somebody cleans the room everyday.
=> The room is cleaned everyday.

2. How do people learn English?
=> How is English learnt?

3. John will collect me at the airport.
=> I will be collected by John at the airport.

4. Mr. Robinson teaches us how to speak English properly.
=> We are taught how to speak English properly by Mr.Robinson.

5. Your teacher must sign this form.
=> This form must be signed by your teacher.

6. People play football all over the world.
=> Football is played all over the world.

7. Our form teacher will hold a class discussion next Monday.
=> A class discussion will be held by our form teacher next Monday.

8. Will you invite her to your birthday party?
=> Will she be invited by you to your birthday party?

9. We can't wear jeans at work.
=> Jeans can't be worn by us at work.

10. Do they speak French and English in Canada?
=> Are French and English spoken in Canada?

I. Rewrite the sentences, use the verbs in present passive form.

1. People can use milk for making butter and cheese.
=> Milk can be used for making butter and cheese.

2. The milkman brings bottles of milk to houses.
=> Bottles of milk are brought to houses by the milkman.

3. Careless driving causes many accidents.
=> Many accidents are caused by careless driving.

4. Weeds cover the river banks.
=> The river banks is covered by weeds.

5. People speak English all over the world.
=> English is spoken all over the world.

6. They don't use the house very often.
=> The house is not used very often.

7. Do they speak French in this school?
=> Is French spoken in this school?

8. They make a lot of beautiful toys from recycled plastic
=> A lot of beautiful toys are made from recycled plastic.

9. The workers clean the streets everyday
=> The streets are cleaned by the workers everyday.

- They [1. work] ...................worked........ very hard when they [ 2.be] ........was............. young.

- I am doing my homework. I can't come with you now. As soon as I [3.do] ........have done.......... all of it. I [4. go]...will.......with you

- It always [5. rain] ........rains....... a lot at the weekends.

- Mrs. Hien [6.go] .........is going.......... to the market. Will You [7. tell] .............tell............ her the news when she [8. come] ......come........back?

- By this time last year, my brother [9. spend] ..............spent............. his summer holiday [10. do] ......doing......... volunteer work in the mountainous areas.

31. Our new teacher has ............an........... oval face with ...........a...... wavy hair.

32. Nga is ..........the...... most sociable person in my class.

33. His father dided of ........a.......... broken heart.

34. I used to work on ........a.........farm. It's in ....the........ north of the country.

35. We mustn't let ....the....... children play in ...the........ kitchen because it's .........a....... dangerous place.

36. What beautiful weather today!