a) Xét \(\Delta\)ADI và \(\Delta\)AHI có:

     AD = AH (gt)

     DI = HI (gt)

    AI: cạnh chung

Do đó \(\Delta\)ADI = \(\Delta\)AHI (c.c.c)

b) Xét \(\Delta\)AHC vuông tại D và \(\Delta\)ABC vuông tại A có ^C chung nên ^HAC = ^B

\(\Delta\)ABC vuông tại A có ^C = 30⁰ nên ^B = 60⁰

Vậy ^HAC = 60⁰

\(\Delta\)AHD có ^HAC = 60⁰ và AH = AD nên \(\Delta\)AHD đều (đpcm)

c)  \(\Delta\)ADI = \(\Delta\)AHI (cmt) suy ra ^DAI = ^HAI (hai góc tương ứng)

Xét \(\Delta\)ADK và \(\Delta\)AHK có:

     AD = AH (gt)

     ^DAI = ^HAI (cmt)

    AK: cạnh chung

Do đó  \(\Delta\)ADK = \(\Delta\)AHK (c.g.c)

=> ^ADK = ^AHK = 90⁰ (hai góc tương ứng)

Kết hợp với AB vuông góc AC suy ra AB//KD (đpcm)

d) Chứng minh được: \(\Delta\)AHB = \(\Delta\)EHK (c.g.c)

=> ^HAB = ^HEK => KE // AB

Khi đó qua K có hai đường thẳng KD, KE song song với AB (trái với tiên đề Ơ - cơ - lít)

Vậy KD trùng KE hay D,K,E thẳng hàng (đpcm)

câu j vậy bạn

Gọi số phút nếu đi với vận tốc trung bình 23 km/h là a

Vì thời gian và vận tốc là hai đại lượng tỉ lệ nghịch nên ta có: 

10 . 20 = a . 23

=> a = 200 / 23

=> a = 8,69.....( làm tròn lak 9 phút )

Vậy nếu đi với vận tốc trung bình 23 km/h thì hết khoảng 7 phút

( mk nghĩ z........nếu cs sai sót gì thì mong you bỏ qua a )

Hello, my name Is Tri, I'm 13 years old. I am from Vietnam, I live in Ha Dong District, Ha Noi, I was the study in Phu La secondary school. My school is small in Van Phu Village, my hobby is playing soccer and play a computer game, my favourite food and drink are chicken fried and Pepsi, and now, I tell about my family, first, my family have four people: my parent, my little brother and my grandmother. My father name's Dung, he's 42 years old, he's tall and he is very fat, his job is ... hmm, I don't know, his hobby is playing chess. My mother name's Trang, she's 40 years old, she is short and thin, her job's expert, her hobby is reading the book, her favourite book is Harry Potter. My little brother name's Tam, he's 7 years old, he studies in Phu La Primary school, he is short and thin( he look a mother ) his hobby is playing a mobile phone game and playing football, my grandmother name's Hoa, she was born in 1950, and now she's 70 years old, she's tall and thin, I don't know her hobby but she's good grandmother. This my family and I

I live in Hanoi with my small family, and there are four of us living together. I have a little sister who is much younger than me. I am now 18, and she is only 12. Her height is just under my shoulders a little bit, and I am sure that she will be much taller than me in the future. My high school and her secondary school are just 20m from each other, so I have the mission to take her to school and pick her up after class.

My mother is a manager of the Human Resources Department of a computer company. She is tall but a little bit chubby, and she has a rather round face that make her look younger than her real age. She is always busy with her work, so we rarely have time to play with her. Sometimes she has to go on a business trip, so there are just three of us take care of each other.

My father is an comic artist, so most of the time he just stays at home to finish his work. He is a thin man with messy black hair, and he has a big pair of glasses on his face. He is funny and always have some jokes that make the whole family laugh. His drawings are beautiful, and he is also a good cook. He takes a very good care of the house since my mother does not have much time, and his food are both delicious and eye – catching.

I love the weekend because it is the only time that my family gathers together. I know my parents have to work hard to support the family, so I will always try my best to be a good daughter and student to make them proud.

a, Xét △BEH có: BE = BH (gt) => △BEH cân tại B => ^E  = ^BHE 

Xét  △BEH có ABC là góc ngoài của tam giác tại đỉnh B => BAC = ^E + ^BHE = 2 . ^E

Mà ABC = 2 . ^C

=> 2 . ^C = 2 . ^E

=> ^C = ^E

Mà ^E  = ^BHE (cmt)

=> ^C = ^BHE 

Mà ^BHE = ^DHC (2 góc đối đỉnh)

=> ^C = ^DHC   (1)

Xét △DHC có: ^DHC = ^C (cmt) => △DHC cân tại D => DC = DH 

Xét △AHC vuông tại H có: ^ACH + ^CAH = 90^o (tổng 2 góc nhọn trong tam giác vuông)

=> ^CAH = 90^o - ^ACH 

=> ^DAH = 90^o - ^DCH (2)

Ta có: ^AHD + ^DHC = 90^o (2 góc phụ nhau)

=> ^AHD  = 90^o - ^DHC (3)

Từ (1) ; (2) ; (3) => ^DAH = ^AHD

Xét △ADH có: ^DAH = ^AHD (cmt) => △ADH cân tại D

b, Xét △EAD có: ^ADE + ^DAE + ^E = 180^o (tổng 3 góc trong tam giác)

Xét △ABC có: ^ABC + ^C + ^BAC = 180^o (tổng 3 góc trong tam giác)

Mà ^C = ^E (cmt) ; ^DAE là góc chung

=> ^ADE = ^ABC

c, Vì ^E = 25^o mà ^E  = ^BHE => ^BHE = 25^o

Ta có: ^AHB + ^BHE = ^AHE

=> 90^o + 25^o = ^AHE 

=> ^AHE = 115^o

Xét △AEH có: ^E + ^AHE + ^HAE = 180^o (tổng 3 góc trong tam giác)

=> 25^o + 115^o + ^HAE = 180^o 

=> ^HAE = 40^o 

a, Do M là trung điểm AC=> AM=MC

Xét  ∆ AMD và  ∆ CMB ta có:

  AM=MC( cmt)

  \(\widehat{AMD}\)=\(\widehat{CMB}\)( đối đỉnh)

MD=BM( gt)

 =>  ∆ AMD= ∆ CMB ( c.g.c)

=>\(\widehat{ADM}\)=\(\widehat{MBC}\)( 2 góc tương ứng)

Mad 2 góc này so le trong

Nên AD//BC.

b, 

Xét  ∆  AMBvà  ∆ CMD ta có:

  AM=MC( cmt)

  \(\widehat{AMB}\)=\(\widehat{CMD}\)( đối đỉnh)

MD=BM( gt)

 =>  ∆ AMB= ∆ CMD ( c.g.c)

=> AB=CD( 2 cạnh tương ứng)

Do  ∆ABC cân tại A => AB=AC

Mà AB=CD (cmt)

Nên AC=CD

Xét ∆ACD có: AC=CD

=>∆ACD cân tại C

Thanks