a/ Tam giác AMN cân tại A (gt). \(\Rightarrow\) \(\widehat{AMN}=\widehat{ANM};AM=AN.\)

Xét tam giác AMB và tam giác ANC có:

+ AM = AN (cmt).

+ \(\widehat{AMB}=\widehat{ANC}\left(\widehat{AMN}=\widehat{ANM}\right).\)

+ MB = NC (gt).

\(\Rightarrow\) Tam giác AMB = Tam giác ANC (c - g - c).

\(\Rightarrow\) AB = AC (cặp cạnh tương ứng).

Xét tam giác ABC có: AB = AC (cmt).

\(\Rightarrow\) Tam giác ABC cân tại A.

b/ Tam giác ABC cân tại A (cmt) \(\Rightarrow\) \(\widehat{ABC}=\widehat{ACB}.\)

Mà \(\widehat{ABC}=\widehat{MBH;}\widehat{ACB}=\widehat{NCK}\text{​​}\) (đối đỉnh).

\(\Rightarrow\) \(\widehat{MBH}=\widehat{NCK}.\)

Xét tam giác MBH và tam giác NCK \(\left(\widehat{BHM}=\widehat{CKN}=90^o\right)\)có:

+ MB = NC (gt).

+ \(\widehat{MBH}=\widehat{NCK}\left(cmt\right).\)

\(\Rightarrow\) Tam giác MBH = Tam giác NCK (cạnh huyền - góc nhọn).

c/ Tam giác MBH = Tam giác NCK (cmt).

\(\Rightarrow\) \(\widehat{BMH}=\widehat{CNK}\) (cặp góc tương ứng).

Xét tam giác OMN có: \(\widehat{NMO}=\widehat{MNO}\) (do \(\widehat{BMH}=\widehat{CNK}\)).

\(\Rightarrow\) Tam giác OMN tại O.

Câu 1:

a: A={x∈R|x>=1}

=>A=[1;+∞)

B={x∈R|x<=3}

=>B=(-∞;3]

A\(\cap\) B=[1;+∞)\(\cap\) (-∞;3]

=[1;3]

A\(\cup\) B=[1;+∞)\(\cup\) (-∞;3]

=(-∞;+∞)

b: A={x∈R|x<=1}

=>A=(-∞;1]

B={x∈R|x>=3}

=>B=[3;+∞)

A\(\cap\) B=(-∞;1]\(\cap\) [3;+∞)

=∅

A\(\cup\) B=(-∞;1]\(\cup\) [3;+∞)

The doctor (already, examine)____________________ the patient.

Marconi (invent)________________ the telephone.

How many French tourists (meet)_______ she __________ last weekend?

They (repair)________________ their house all this month.

You (work)______________ too hard! That’s why you are tired.

When the doorbell (ring)_________, I (get)______ up and (answer)________it.

We (know)______________ her for years.

Her parents (live)__________ in Hue from 1985 to 1996.

The plant I bought (grow)______________ very much. And I water it every day.

We (meet)_________________ at 10 o’clock tonight.

Kate looks much thinner. She (lose)_____________ a lot of weight.

Look at those black clouds! It (rain)______________________.

Look! The fire engine (arrive)_________________.

Run! The bus driver (wait)_________________ for us!

Watch the baby! He (fall)__________________ off the bed.

Look at the sun! It (be)__________________ a very hot day!

It’s 7:30 in the morning and Mr. Brown (drive)_______________ to work, as usual.

Hurry up! We (miss)______________________ the train.

I (brush)_____________________ my teeth, have a wash and go to bed.

I (not have)_________________ breakfast this morning.

Câu 2: 

#include <bits/stdc++.h>

using namespace std;

long long n,i,x,nn;

int main()

{

cin>>n>>x;

nn=x;

for (i=2; i<=n; i++)

{

cin>>x;

nn=min(nn,x);

}

cout<<nn;

return 0;

}

b: \(\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right):\dfrac{a-1}{\sqrt{a}+1}\)

\(=\left(a-2\sqrt{a}+1\right)\cdot\dfrac{\left(\sqrt{a}+1\right)}{a-1}\)

\(=\sqrt{a}-1\)

Câu 1:

a: A={x∈R|x>=1}

=>A=[1;+∞)

B={x∈R|x<=3}

=>B=(-∞;3]

A\(\cap\) B=[1;+∞)\(\cap\) (-∞;3]

=[1;3]

A\(\cup\) B=[1;+∞)\(\cup\) (-∞;3]

=(-∞;+∞)

b: A={x∈R|x<=1}

=>A=(-∞;1]

B={x∈R|x>=3}

=>B=[3;+∞)

A\(\cap\) B=(-∞;1]\(\cap\) [3;+∞)

=∅

A\(\cup\) B=(-∞;1]\(\cup\) [3;+∞)

Câu 2:

A=(-3;5]\(\cup\) [8;10]\(\cup\) (2;8)

=(-3;10]

B=[0;2]\(\cup\) (-∞;5]\(\cup\) (1;+∞)

=(-∞;+∞)

C=[-4;7]\(\cup\) (0;10)

=[-4;10)

D=(-∞;3]\(\cup\) (-5;+∞)

=(-∞;+∞)

E=(3;+∞)\(-∞;1]

=(3;+∞)

F=(1;3]\[0;4)

=∅