Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCGCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Bài 2:
a: Xét ΔADB vuông tại D và ΔAEC vuông tại E có
AB=AC
\(\widehat{A}\) chung
Do đó: ΔADB=ΔAEC
Suy ra: AD=AE
hayΔADE cân tại A
b: Xét ΔABC có
AE/AB=AD/AC
nên DE//BC
c: Xét ΔEBC vuông tại E và ΔDCB vuông tại D có
EC=DB
BC chung
Do đó: ΔEBC=ΔDCB
Suy ra: \(\widehat{IBC}=\widehat{ICB}\)
hay ΔIBC cân tại I
d: Xét ΔAEI vuông tại E và ΔADI vuông tại D có
AI chung
AE=AD
Do đó: ΔAEI=ΔADI
Suy ra: \(\widehat{BAI}=\widehat{CAI}\)
=>AK là tia phân giác của góc BAC
Ta có: ΔABC cân tại A
mà AK là đường phân giác
nên AK là đường cao
a: Xét ΔBEC vuông tại E và ΔCDB vuông tại D có
BC chung
\(\widehat{EBC}=\widehat{DCB}\)
Do đó: ΔBEC=ΔCDB
b: Xét ΔABD vuông tại D và ΔACE vuông tại E có
AB=AC
BD=CE
Do đó: ΔABD=ΔACE
Xét ΔBEK vuông tại E và ΔCDK vuông tại D có
EB=DC
\(\widehat{EBK}=\widehat{DCK}\)
Do đó: ΔBEK=ΔCDK
c: Xét ΔBAK và ΔCAK có
BA=CA
AK chung
BK=CK
Do đó: ΔBAK=ΔCAK
Suy ra: \(\widehat{BAK}=\widehat{CAK}\)
hay AK là tia phân giác của góc BAC
mk ko biết cách vẽ hình trên olm nên bạn thông cảm
Vì d ko cắt BC => đường thẳng d // BC
=> \(\widehat{DAB}=\widehat{BAC},\widehat{DBC}=90^0\)
Xét tam giác ABC có \(\widehat{BAC}+\widehat{ABC}+\widehat{ACB}=180^0\)
=> \(\widehat{ABC}+\widehat{ACB}=90^0\)
=> \(\widehat{ABC}=90^0-\widehat{ACB}\)(1)
Ta lại có \(\widehat{DBC}=90^0\)=> \(\widehat{DAB}+\widehat{ABC}=90^0\)
=> \(\widehat{ABC}=90^0-\widehat{DAB}\)(2)
Từ 1,2 => \(\widehat{ACB}=\widehat{DAB}\)
mà \(\widehat{ABC}=\widehat{ACB}\)( Vì tam giác ABC cân tại A)
=> \(\widehat{DBA}=\widehat{ABC}\)
Mặt khác \(\widehat{DAB}=\widehat{ABC}\)(\(d//BC\))
=> \(\widehat{DAB}=\widehat{DBA}\)
=> tam giác DAB cân tại D => DA=DB
Tương tự : AE=EC
=> BD + CE =AD+AE
=> BD+CE = DE (đpcm)
Ta có d đi qua A, D và E thuộc d
=>D, A, E thẳng hàng =>^DAB+^BAC+^CAE=180° =>^DAB+^CAE=90°(1)
Xét tam giác DAB vuông ở D =>^DBA+^DAB=90°(2)
Từ (1) và (2) =>^CAE=^DAB
Xét tam giác BAD và tam giác ACE có: ^DAB=^CAE(cmt)
AB=AC(tam giác ABC cân) ^ADB=^AEC(=90°)
=>Tam giác BAD tam giác ACE(g.c.g)
=> BD=AE; EC=AD
Mà DE=AD+AE
=>DE=BD+CE
