Cho tam giác ABC cân tại A, đường cao AH, kẻ \(HD\perp AC\) (\(D\in AC\) ). Gọi I là trung điểm của HD, M là trung điểm của CD. Chứng minh: \(AH\perp HM\)

Cho tam giác ABC cân tại A, đường cao AH. Gọi M là trung điểm của AH. D là giao điểm của CM với AB. Gọi N là trung điểm của BD.

a) Chứng minh HN // CD

b) Chứng minh \(AD=\frac{1}{3}AB\)

Cho tam giác ABC có \(\widehat{B}=60^o\) và một đường thẳng (d) vuông góc với BA tại A. Phân giác góc B cắt (d) và cắt đường cao AH tại I.

a) tam giác ABD là tam giác gì? Vì sao ?

b) Chứng minh tam giác AID là tam giác đều

c) Hạ DK vuông góc với BC, trên tia IH lấy điểm E sap cho HE = HI. Chứng minh ADKE là hình thang cân

Read the text and look carefully at each line. Tick (T) the lines which are correct and pick out the unnecessary words. There are two examples at the beginning (0 and 00). Write your answers on the right lines provided.

Dear John,

Thank you for your letter which has arrived last week. I’m sorry I 0. has

haven’t written to you for two months. I’ve been so busy as college, 00. T

I simply haven’t had time. Don’t be angry with me!

Do you like the English family you are been staying with? Have you 1. ___

being started your new English course yet? Do your teachers give 2. ___

you a lot of homework? I hope not, but I expect they do. Anyway 3. ___

don’t be forget, I can’t help you with it if it’s difficult. And what about 4. ___

London? Have you been on the underground yet? 5. ___

You will never guess what was happened to me last week. It was 6. ___

Tuesday morning, and I was walking along the road near my house, 7. ___

When suddenly two men with guns rushed out of the bank. I went to 8. ___

The nearest phone box and rang to the police. Unfortunately, the bank 9. ___

Robbers escaped before they were arrived. It was very exciting! 10. ___

Now it’s your turn to write! Have fun!

Best wishes,

Thomas.

Complete the second sentence in such a way that it has the same meaning as the one before it, using the word given. DO NOT CHANGE THE WORD GIVEN.

She could not type the report in time. (be)

=> The report ............................. in time.

1. Choose the word which is stressed on the first syllable
A. prefer
B. cartoon
C. curiosity
D. necessary
2. Choose the word with the different stress pattern.
A. again
B. before
C. center
D. reverse
3. Choose the word with the different stress pattern.
A. typical
B. holiday
C. mechanic
D. celebrate

Chứng minh rằng:

a) \(-x^2+6x-10< 0\) với mọi x

b) \(x^2+x+1>0\) với mọi x

c) \(4x^2+y^2+4xy+4x+2y+2\ge0\) với mọi x, y

\(\left(x+2\right)^2-\left(x-1\right)^2=27\)