a)xét ΔBEA và ΔBEC có:

\(\widehat{BEC}=\widehat{BEA}=90^o\)

AB=BC(ΔABC cân tại B)

\(\widehat{BCE}=\widehat{BAE}\)(ΔABC cân tại B)

⇒ΔBEA=ΔBEC (c.huyền.g.nhọn)

b)vì ΔBEA=ΔBEC nên AE=CE(2 cạnh tương ứng)

⇒E là trung điểm của AC

⇒BE là đường trung tuyến của ΔABC (đ.p.ch/m)₍₁₎

c) Ta có:

vì D là trung điểm của BC⇒AD là đường trung tuyến của ΔABC₍₂₎

từ (1)và(2) ⇒K là trọng tâm của ΔABC

⇒KD=\(\dfrac{1}{2}KA\)

xét ΔABK có:

KB+KA>AB(bất đẳng thức tam giác)

hay KB+2KD>AB

mà AB=BC

⇒KB+2KD>BC(đ.p.ch/m)

a: Xét ΔAIB và ΔAID có 

AI chung

\(\widehat{BAI}=\widehat{DAI}\)

AB=AD

Do đó: ΔAIB=ΔAID

Bài 3:

Nếu đáy lớn được tăng thêm 5 cm thì diện tích sẽ tăng một phần bằng 5 x chiều cao : 2

Vậy chiều cao của hình thang là:
$20\times 2:5=2$ (m) 

Diện tích hình thang ban đầu là:

$50\times 2:2=50$ (m²)

Refer

1. “Your cousin speaks English very well” Paul told me

Paul said that ___________my cousin spoke English very well____________

2. “The man broke out of prison yesterday” said the policeman

The policeman told us_that the man had broken out of prison the day beforr__

3. “I’ll lend you this book as soon as I finish it” Owen said to me

Owen said __me that he would lend me that book as soon as he finished it___

4. “I think I forgot to turn off the lights this morning” Brenda told Brian

Brenda told Brian ____that he thought he had forgotten to turn off the lights that morning.____

5. “I work eight hours a day, except when the children are on holiday” said Mrs. Wood

Mrs. Wood said me that he worked eight hours a day, excepted when the children were on holiday

6. “You’ve been making good progress this semester” Miss Lynn told me

Miss Lynn said that _____I had been making good progress that semester_________

7. “If you bought all the tickets, you would win the lottery” the man said

The man told me ______that If I had bought all the tickets, I would win the lottery______________

8. “I like swimming but I don’t go very often” Jill said to Pam

Jill said that ______he liked swimming but he didn’t go very often___________________________

9. “I want to buy it, but I haven’t brought any money” said Patrick

Patrick told me _________that he wanted to buy it, but he hadn’t brought any money_______________________

10. “I’m going to visit my aunt in Hue, but I’m not sure when” said Mai

Mai told me _________that she was going to visit her aunt in Hue, but she was not sure when__________________

Bài 1:

Cường độ dòng điện qua điện trở: I = U : R = 12 : 60 = 0,2 (A)

Bài 2:

Điện trở tương đương: R_tđ = R₁ + R₂ = 3 + 5 = 8 (\(\Omega\))

Cường độ dòng điện qua mạch chính: I = U : R_tđ = 12 : 8 = 1,5 (A)

Bài 3:

Điện trửo tương đương: R_tđ = (R₁.R₂) : (R₁ + R₂) = (3.6) : (3 + 6) = 2 (\(\Omega\))

Có: U = U₁ = U₂ = 12V (Vì R₁//R₂)

Cường độ dòng điện qua mạch chính và các mạch rẽ:

I = U : R_tđ = 12 : 2 = 6 (A)

I₁ = U₁ : R₂ = 12 : 3 = 4(A)

I₂ = U₂ : R₂ = 12 : 6 = 2(A)

Bài 3: 

52,38-2,1=50,28

45+85,69=130,69

7,14x82=585,48

9,03:2,1=4,3

\(\Leftrightarrow2\left(x+1\right)^3=56\Leftrightarrow\left(x+1\right)^3=28\Leftrightarrow\)

2:

1+cot^2a=1/sin^2a

=>1/sin^2a=1681/81

=>sin^2a=81/1681

=>sin a=9/41

=>cosa=40/41

tan a=1:40/9=9/40