c/

$C=\frac{11}{2}(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{91.93})$

$=\frac{11}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+...+\frac{93-91}{91.93}\right)$

$=\frac{11}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{91}-\frac{1}{93}\right)$

$=\frac{11}{2}(1-\frac{1}{93})$

$=\frac{11}{2}.\frac{92}{93}=\frac{506}{93}$

d/

$D=5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{675}\right)$

$=\frac{5}{2}\left(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{675}\right)$

$=\frac{5}{2}\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{27-25}{25.27}\right)$

$=\frac{5}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{25}-\frac{1}{27}\right)$
$=\frac{5}{2}\left(1-\frac{1}{27}\right)$
$=\frac{5}{2}.\frac{26}{27}=\frac{65}{27}$

e/

$E=13\left(\frac{1}{15}+\frac{1}{35}+\frac{1}{63}...+\frac{1}{1023}\right)$

$=\frac{13}{2}\left(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{1023}\right)$

$=\frac{13}{2}\left(\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{33-31}{31.33}\right)$

$=\frac{13}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{31}-\frac{1}{33}\right)$
$=\frac{13}{2}(\frac{1}{3}-\frac{1}{33})=\frac{65}{33}$
$=\frac{5}{2}.\frac{26}{27}=\frac{65}{27}$

Xet tam giac BDC va tam giac CEB ta co 

^BDC = ^CEB = 90⁰

BC _ chung 

^BCD = ^CBE ( gt ) 

=> tam giac BDC = tam giac CEB ( ch - gn ) 

=> ^DBC = ^ECB ( 2 goc tuong ung ) 

Ta co ^B - ^DBC = ^ABD 

^C - ^ECB = ^ACE 

=> ^ABD = ^ACE 

Xet tam giac IBE va tam giac ICD 

^ABD = ^ACE ( cmt )

^BIE = ^CID ( doi dinh ) 

^BEI = ^IDC = 90⁰

Vay tam giac IBE = tam giac ICD (g.g.g) 

c, Do BD vuong AC => BD la duong cao 

CE vuong BA => CE la duong cao 

ma BD giao CE = I => I la truc tam 

=> AI la duong cao thu 3 

=> AI vuong BC 

Câu 58: B

Câu 59: C

8. As it is raining heavily, we can't go on a picnic

9. I suggest (that) you should get a plumber to check the pipes

10. If you don't succeed, you'll have to try it again

11. If she had enough money, she would buy the dictionary

12. I suggest using gas instead of burning coal

13. I suggest you should install a burglar alarm in your house

14. If we recycle, we will save natural resources

15. If you don't hurry up, you will be late for work

16. If you work too much, you will be tired

17. I suggest putting different kinds of.....

18. Lan broke the glass as she was careless

19. If you litter the place around you, it will be a junk yard

20. Paul suggested using public transportation

21. If she doesn't reduce the use of water and electricity, she will have to.....

22. Since the weather was snowy, we postponed our soccer match

23. Tan suggested that Lam should buy a car

24. Lan suggested that I should look for another job

25. The scientist suggested using public transportation instead of private vehicles

26. giống c12

27. The principle is pleased that the students in grade 9 are good helpers

28. If we put garbage into the bins, we will minimize pollution

29. If you are careless, you will broke the vase

30. If you don't stop cutting trees, I will call the police

31. If you use electricity to catch fish, you will be fined heavily

32. I'm sure that that boy will have a test.....

33. We are disappointed that you threw the rubbish on the street

34. It is extremely important that all of us work together to protect the environment

35. I'm sorry that I couldn't do anything to help you

36. He is sure that environmental pollution in this area can be controlled

37. She was annoyed that he damaged the car yesterday

Bài 2: 

a: Xét ΔABC có

X là trung điểm của BC

Y là trung điểm của AB

Do đó: XY là đường trung bình

=>XY//AC và XY=AC/2=3,5(cm)

hay XZ//AC và XZ=AC

b: Xét tứ giác AZBX có 

Y là trung điểm của AB

Y là trung điểm của ZX

Do đó: AZBX là hình bình hành

mà \(\widehat{AXB}=90^0\)

nên AZBX là hình chữ nhật

d: Xét tứ giác AZXC có

XZ//AC

XZ=AC

Do đó: AZXC là hình bình hành